Linear Algebra With Applications (classic Version)
5th Edition
ISBN: 9780135162972
Author: BRETSCHER, OTTO
Publisher: Pearson Education, Inc.,
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 5.2, Problem 32E
Find an orthonormal basis of the plane
Expert Solution & Answer
Trending nowThis is a popular solution!
Learn your wayIncludes step-by-step video
schedule02:52
Students have asked these similar questions
Wendy is looking over some data regarding the strength, measured in Pascals (Pa), of some rope and how the strength relates to the number of woven strands in the rope. The data are represented by the exponential function f(x) = 2x, where x is the number of woven strands. Explain how she can convert this equation to a logarithmic function when strength is 256 Pascals.
Please type out answer
Harrison and Sherrie are making decisions about their bank accounts. Harrison wants to deposit $200 as a principal amount, with an interest of 2% compounded quarterly. Sherrie wants to deposit $200 as the principal amount, with an interest of 4% compounded monthly. Explain which method results in more money after 2 years. Show all work.
Please type out answer
Mike is working on solving the exponential equation 37x = 12; however, he is not quite sure where to start. Solve the equation and use complete sentences to describe the steps to solve.
Hint: Use the change of base formula: log y =
log y
log b
Chapter 5 Solutions
Linear Algebra With Applications (classic Version)
Ch. 5.1 - Find the length of each of the vector vin...Ch. 5.1 - Find the length of each of the vector vin...Ch. 5.1 - Find the length of each of the vector vin...Ch. 5.1 - Find the angle between each of the pairs of...Ch. 5.1 - Find the angle between each of the pairs of...Ch. 5.1 - Find the angle between each of the pairs of...Ch. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - For each pair of vectors u,vlisted in Exercises 7...Ch. 5.1 - For which value(s) the constant k are the vectors...
Ch. 5.1 - Considerthevector u=[131] and v=[100] in n . a....Ch. 5.1 - Give an algebraic proof for thetriangleinequality...Ch. 5.1 - Leg traction. The accompanying figure shows how a...Ch. 5.1 - Leonardo da Vinci and the resolution of forces....Ch. 5.1 - Consider thevector v=[1234] in 4 . Find a basis of...Ch. 5.1 - Consider the vectors...Ch. 5.1 - Find a basis for W , where W=span([1234],[5678]).Ch. 5.1 - Here is an infinite-dimensional version of...Ch. 5.1 - For a line L in 2 , draw a sketch to interpret the...Ch. 5.1 - Refer to Figure 13 of this section. The least-s...Ch. 5.1 - Find scalara, b, c, d, e, f,g such that the...Ch. 5.1 - Consider a basis v1,v2,...,vm of a subspace V of n...Ch. 5.1 - Prove Theorem 5.1 .8d. (V)=V for any subspace V of...Ch. 5.1 - Prob. 24ECh. 5.1 - a. Consider a vector v in n , and a scalar k. Show...Ch. 5.1 - Find the orthogonal projection of [494949] onto...Ch. 5.1 - Find the orthogonal projection of 9e1 onto the...Ch. 5.1 - Find the orthogonal projection of [1000] onto the...Ch. 5.1 - Prob. 29ECh. 5.1 - Consider a subspace V of n and a vector x in n...Ch. 5.1 - Considerthe orthonormal vectors u1,u2,...um , in n...Ch. 5.1 - Consider two vectors v1 and v2 in n . Form the...Ch. 5.1 - Among all the vector in n whose components add up...Ch. 5.1 - Among all the unit vectors in n , find the one for...Ch. 5.1 - Among all the unit vectors u=[xyz] in 3 , find...Ch. 5.1 - There are threeexams in your linear algebra class,...Ch. 5.1 - Consider a plane V in 3 with orthonormal basis...Ch. 5.1 - Consider three unit vectors v1,v2 , and v3 in n ....Ch. 5.1 - Can you find a line L in n and a vector x in n...Ch. 5.1 - In Exercises 40 through 46, consider vectors...Ch. 5.1 - In Exercises 40 through 46, consider vectors...Ch. 5.1 - In Exercises 40 through 46, consider vectors...Ch. 5.1 - In Exercises 40 through 46, consider vectors...Ch. 5.1 - In Exercises 40 through 46, consider vectors...Ch. 5.1 - In Exercises 40 through 46, consider vectors...Ch. 5.1 - In Exercises 40 through 46, consider vectors...Ch. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Prob. 7ECh. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Prob. 9ECh. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Using paper and pencil, perform the Gram-Schmidt...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Using paper and pencil, find the QR factorization...Ch. 5.2 - Perform the Gram—Schmidt process on the...Ch. 5.2 - Consider two linearly independent vector v1=[ab]...Ch. 5.2 - Perform the Gram-Schmidt process on the...Ch. 5.2 - Find an orthonormal basis of the plane x1+x2+x3=0Ch. 5.2 - Find an orthonormal basis of the kernel of the...Ch. 5.2 - Find an orthonormal basis of the kernel of the...Ch. 5.2 - Find an orthonormal basis of the kernel of the...Ch. 5.2 - Consider the matrix M=12[111111111111][235046007]...Ch. 5.2 - Consider the matrix...Ch. 5.2 - Find the QR factorization of A=[030000200004] .Ch. 5.2 - Find an orthonormal basis u1,u2,u3 of 3 such that...Ch. 5.2 - Consider an invertible nn matrix A whose...Ch. 5.2 - Consider an invertible upper triangular nn matrix...Ch. 5.2 - The two column vectors v1 and v2 of a 22 matrix...Ch. 5.2 - Consider a block matrix A=[A1A2] with linearly...Ch. 5.2 - Consider an nm matrix A with rank(A)m . Is it...Ch. 5.2 - Consider an nm matrix A with rank(A)=m . Is...Ch. 5.3 - Which of the matrices in Exercises 1 through 4 are...Ch. 5.3 - Which of the matrices in Exercises 1 through 4 are...Ch. 5.3 - Which of the matrices in Exercises 1 through 4 are...Ch. 5.3 - Which of the matrices in Exercises 1 through 4 are...Ch. 5.3 - If the nnmatrices A and B are orthogonal, which of...Ch. 5.3 - If the nnmatrices A and B are orthogonal, which of...Ch. 5.3 - If the nnmatrices A and B are orthogonal, which of...Ch. 5.3 - If the nnmatrices A and B are orthogonal, which of...Ch. 5.3 - If the nnmatrices A and B are orthogonal, which of...Ch. 5.3 - If the nnmatrices A and B are orthogonal, which of...Ch. 5.3 - If the nnmatrices A and B are orthogonal, which of...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - If the nnmatrices A and B are symmetric and B is...Ch. 5.3 - IfA andB are arbitrary nnmatrices, which of the...Ch. 5.3 - If A and B are arbitrary nnmatrices, which of the...Ch. 5.3 - If A and B are arbitrary nnmatrices, which of the...Ch. 5.3 - If A and B are arbitrary nnmatrices, which of the...Ch. 5.3 - If A and B are arbitrary nnmatrices, which of the...Ch. 5.3 - If A and B are arbitrary nnmatrices, which of the...Ch. 5.3 - Consider an nn matrix A, a vector v in m , and...Ch. 5.3 - Consider an nn matrix A. Show that A is an...Ch. 5.3 - Show that an orthogonal transformation L from n to...Ch. 5.3 - Consider a linear transformation L from m to n...Ch. 5.3 - Are the rows of an orthogonal matrix A...Ch. 5.3 - a. Consider an nm matrix A such that ATA=Im . Is...Ch. 5.3 - Find all orthogonal 22 matrices.Ch. 5.3 - Find all orthogonal 33 matrices of theform...Ch. 5.3 - Find an orthogonal transformation T form 3 to 3...Ch. 5.3 - Find an orthogonal matrix of the form [2/31/...Ch. 5.3 - Is there an orthogonal transformation T from 3 to...Ch. 5.3 - a. Give an example of a (nonzero) skew-symmetric...Ch. 5.3 - Consider a line L in n , spanned by a unit vector...Ch. 5.3 - Consider the subspace W of 4 spanned by the vector...Ch. 5.3 - Find the matrix A of the orthogonal projection...Ch. 5.3 - Let A be the matrix of an orthogonal projection....Ch. 5.3 - Consider a unit vector u in 3 . We define the...Ch. 5.3 - Consider an nm matrix A. Find...Ch. 5.3 - For which nm matrices A docs theequation...Ch. 5.3 - Consider a QRfactorizationM=QR . Show that R=QTM .Ch. 5.3 - If A=QR is a QR factorization, what is the...Ch. 5.3 - Consider an invertible nn matrix A. Can you write...Ch. 5.3 - Consider an invertible nn matrix A. Can you write...Ch. 5.3 - a. Find all nn matrices that are both orthogonal...Ch. 5.3 - a. Consider the matrix product Q1=Q2S , where both...Ch. 5.3 - Find a basis of the space V of all symmetric 33...Ch. 5.3 - Find a basis of the space V of all skew-symmetric...Ch. 5.3 - Find the dimension of the space of alt...Ch. 5.3 - Find the dimension of the space of all symmetric...Ch. 5.3 - Is the transformation L(A)=AT from 23 to 32...Ch. 5.3 - Is the transformation L(A)=AT from mn to nm...Ch. 5.3 - Find image and kernel of the linear transformation...Ch. 5.3 - Find theimage and kernel of the linear...Ch. 5.3 - Find the matrix of the linear transformation...Ch. 5.3 - Find the matrix of the lineartransformation...Ch. 5.3 - Consider the matrix A=[111325220] with...Ch. 5.3 - Consider a symmetric invertible nn matrix A...Ch. 5.3 - This exercise shows one way to define the...Ch. 5.3 - Find all orthogonal 22 matrices A such that all...Ch. 5.3 - Find an orthogonal 22 matrix A such that all the...Ch. 5.3 - Consider a subspace V of n with a basis v1,...,vm...Ch. 5.3 - The formula A(ATA)1AT for 11w matrix of an...Ch. 5.3 - In 4 , consider the subspace W spanned by the...Ch. 5.3 - In all parts of this problem, let V be the...Ch. 5.3 - An nn matrix A is said to be a Hankel, matrix...Ch. 5.3 - Consider a vector v in n of theform v=[11a2an1]...Ch. 5.3 - Let n be an even positive integer. In both parts...Ch. 5.3 - For any integer m, we define the Fibonacci number...Ch. 5.4 - Consider the subspaceim(A) of 2 , where A=[2436] ....Ch. 5.4 - Consider the subspace im(A) of 3 , where...Ch. 5.4 - Considerasubspace V of n . Let v1,...,vp be a...Ch. 5.4 - Let A bean nm matrix. Is the formula ker(A)=im(AT)...Ch. 5.4 - Let V be the solution space of the linear system...Ch. 5.4 - If A is an nm matrix, is the formula im(A)=im(AAT)...Ch. 5.4 - Consider a symmetric nn matrix A. What is the...Ch. 5.4 - Consider a linear transformation L(x)=Ax from n to...Ch. 5.4 - Consider the linear system Ax=b , where A=[1326]...Ch. 5.4 - Consider a consistent system Ax=b . a. Show that...Ch. 5.4 - Consider a linear transformation L(x)=Ax from n to...Ch. 5.4 - Using Exercise 10 as a guide, define theterm...Ch. 5.4 - Consider a linear transformation L(x)=Ax from n to...Ch. 5.4 - In the accompanying figure, we show the kernel and...Ch. 5.4 - Consider an mn matrix A with ker(A)={0} . Showthat...Ch. 5.4 - Use the formula (imA)=ker(AT) to prove theequation...Ch. 5.4 - Does the equation rank(A)=rank(ATA) hold for all...Ch. 5.4 - Does the equation rank(ATA)=rank(AAT) hold for all...Ch. 5.4 - Find the least-squares solution x* of the system...Ch. 5.4 - By using paper and pencil, find the least-squares...Ch. 5.4 - Find the least-squares solution x* of the system...Ch. 5.4 - Find the least-squares solution x* of the system...Ch. 5.4 - Find the least-squares solution x* of the system...Ch. 5.4 - Find the least-squares solution x* of the system...Ch. 5.4 - Find the least-squares solution x* of the system...Ch. 5.4 - Find the least-squares solution x* of the system...Ch. 5.4 - Consider an inconsistent linear system Ax=b ,...Ch. 5.4 - Consider an orthonormal basis u1,u2,...,un , in n...Ch. 5.4 - Find theleast-squares solution of the system Ax=b...Ch. 5.4 - Fit a linear function of the form f(t)=c0+c1t...Ch. 5.4 - Fit a linear function of the form f(t)=c0+c1t to...Ch. 5.4 - Fit a quadratic polynomial to the data points...Ch. 5.4 - Find the trigonometric function of the form...Ch. 5.4 - Find the function of the form...Ch. 5.4 - Suppose you wish to fit a function of the form...Ch. 5.4 - Let S (t) be the number of daylight hours on the t...Ch. 5.4 - Prob. 37ECh. 5.4 - In the accompanying table, we list the height h,...Ch. 5.4 - In the accompanying table, we list the estimated...Ch. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.5 - In C[a,b] , define the product f,g=abf(t)g(t)dt ....Ch. 5.5 - Does the equation f,g+h=f,g+f,h hold for all...Ch. 5.5 - Consider a matrix S in nn . In n , define the...Ch. 5.5 - In nm , consider the inner product A,B=trace(ATB)...Ch. 5.5 - Is A,B=trace(ABT) an inner product in nm ?(The...Ch. 5.5 - a. Consider an nm matrix P and an mn matrixQ. Show...Ch. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Consider the space P2 with inner product...Ch. 5.5 - Prob. 11ECh. 5.5 - Prob. 12ECh. 5.5 - For a function f in C[,] (with the inner...Ch. 5.5 - Which of the following is an inner product in P2...Ch. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Consider the linear space P of all polynomials,...Ch. 5.5 - Prob. 25ECh. 5.5 - Prob. 26ECh. 5.5 - Find the Fourier coefficients of the piecewise...Ch. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Gaussian integration,In an introductory...Ch. 5.5 - In the space C[1,1] , we introduce the inner...Ch. 5.5 - a. Let w(t) be a positive-valued function in...Ch. 5.5 - In the space C[1,1] , we define the inner product...Ch. 5.5 - In this exercise, we compare the inner products...Ch. 5 - If T is a linear transformation from n to n...Ch. 5 - If A is an invertible matrix, then the equation...Ch. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - All nonzero symmetric matrices are invertible.Ch. 5 - Prob. 8ECh. 5 - If u is a unit vector in n , and L=span(u) , then...Ch. 5 - Prob. 10ECh. 5 - Prob. 11ECh. 5 - Prob. 12ECh. 5 - If matrix A is orthogonal, then AT must be...Ch. 5 - If A and B are symmetric nn matrices, then AB...Ch. 5 - Prob. 15ECh. 5 - If A is any matrix with ker(A)={0} , then the...Ch. 5 - If A and B are symmetric nn matrices, then...Ch. 5 - Prob. 18ECh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - If A is a symmetric matrix, vector v is in the...Ch. 5 - The formula ker(A)=ker(ATA) holds for all matrices...Ch. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - If A is an invertible matrix such that A1=A , then...Ch. 5 - Prob. 34ECh. 5 - The formula (kerB)=im(BT) holds for all matrices...Ch. 5 - The matrix ATA is symmetric for all matrices A.Ch. 5 - If matrix A is similar to B and A is orthogonal,...Ch. 5 - Prob. 38ECh. 5 - If matrix A is symmetric and matrix S is...Ch. 5 - If A is a square matrix such that ATA=AAT , then...Ch. 5 - Any square matrix can be written as the sum of a...Ch. 5 - If x1,x2,...,xn are any real numbers, then...Ch. 5 - If AAT=A2 for a 22 matrix A, then A must...Ch. 5 - If V is a subspace of n and x is a vector in n ,...Ch. 5 - If A is an nn matrix such that Au=1 for all...Ch. 5 - If A is any symmetric 22 matrix, then there must...Ch. 5 - There exists a basis of 22 that consists of...Ch. 5 - If A=[1221] , then the matrix Q in the QR...Ch. 5 - There exists a linear transformation L from 33 to...Ch. 5 - If a 33 matrix A represents the orthogonal...
Additional Math Textbook Solutions
Find more solutions based on key concepts
In Exercises 25–28, use the confidence interval to find the margin of error and the sample mean.
25. (12.0, 14....
Elementary Statistics: Picturing the World (7th Edition)
Drug for Nausea Ondansetron (Zofran) is a drug used by some pregnant women for nausea. There was some concern t...
Introductory Statistics
Identify f as being linear, quadratic, or neither. If f is quadratic, identify the leading coefficient a and ...
College Algebra with Modeling & Visualization (5th Edition)
16. Coke Cans Assume that cans of Coke are filled so that the actual amounts are normally distributed with a me...
Elementary Statistics (13th Edition)
Limits with trigonometric functions Find the limits in Exercises 43–50.
47.
University Calculus: Early Transcendentals (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Using logarithmic properties, what is the solution to log3(y + 5) + log36 = log366? Show all necessary steps.arrow_forward4.2 Comparing Linear and Exponential Change 7) Money is added to (and never removed from) two different savings accounts (Account A and Account B) at the start of each month according to different mathematical rules. Each savings account had $500 in it last month and has $540 in it this month. (a) Assume the money in Account A is growing linearly: How much money will be in the account next month? How much money was in the account two months ago? How long will it take for the account to have at least $2500? Write an equation relating the amount of money in the account and the number of months from now. Clearly define the meaning of each variable in your equation, and interpret the meaning of each constant in your equation. (b) Assume the money in Account B is growing exponentially. How much money will be in the account next month? How much money was in the account two months ago? How long will it take for the account to have at least $2500? Write an equation relating the amount of money…arrow_forwardWhich of the following is the solution to the equation 25(z − 2) = 125? - Oz = 5.5 Oz = 3.5 Oz = -2.5 z = -0.5arrow_forward
- Analyze the graph below to identify the key features of the logarithmic function. 2 0 2 6 8 10 12 2 The x-intercept is y = 7, and the graph approaches a vertical asymptote at y = 6. The x-intercept is x = 7, and the graph approaches a vertical asymptote at x = 6. The x-intercept is y = -7, and the graph approaches a vertical asymptote at y = −6. The x-intercept is x = -7, and the graph approaches a vertical asymptote at x = −6.arrow_forwardCompare the graphs below of the logarithmic functions. Write the equation to represent g(x). 2 f(x) = log(x) 2 g(x) -6 -4 -2 ° 2 0 4 6 8 -2 - 4 g(x) = log(x) - g(x) = log(x) + 4 g(x) = log(x+4) g(x) = log(x-4) -2 -4 -6arrow_forwardWhich of the following represents the graph of f(x)=3x-2? 3 2 • 6 3 2 0- 0- • 3 2 0 -2 3arrow_forward
- 2) Suppose you start with $60 and increase this amount by 15%. Since 15% of $60 is $9, that means you increase your $60 by $9, so you now have $69. Notice that we did this calculation in two steps: first we multiplied $60 by 0.15 to find 15% of $60, then we added this amount to our original $60. Explain why it makes sense that increasing $60 by 15% can also be accomplished in one step by multiplying $60 times 1.15. 3) Suppose you have $60 and want to decrease this amount by 15%. Since 15% of $60 is $9, that means you will decrease your $60 by $9, so you now have $51. Notice that we did this calculation in two steps: first we multiplied $60 by 0.15 to find 15% of $60, then we subtracted this amount from our original $60. Explain why it makes sense that decreasing $60 by 15% can also be accomplished in one step by multiplying $60 times 0.85. 4) In the Read and Study section, we noted that the population in Colony B is increasing each year by 25%. Which other colony in the Class Activity…arrow_forward5) You are purchasing a game for $30. You have a 5% off coupon and sales tax is 5%. What will your final price be? Does it matter if you take off the coupon first or add in the tax first? 6) You have ten coupons that allow you to take 10% off the sales price of a jacket, and for some strange reason, the store is going to allow you to use all ten coupons! Does this mean you get the jacket for free? Let's really think about what would happen at the checkout. First, the teller would scan the price tag on the jacket, and the computer would show the price is $100. After the teller scans the first coupon, the computer will take 10% off of $100, and show the price is $90. (Right? Think about why this is.) Then after the teller scans the second coupon, the computer will take 10% off of $90. (a) Continue this reasoning to fill in the table below showing the price of the jacket (y) after you apply x coupons. (b) Make a graph showing the price of the jacket from x = 0 to x = 10 coupons applied.…arrow_forward(a) (b) (c) (d) de unique? Answer the following questions related to the linear system x + y + z = 2 x-y+z=0 2x + y 2 3 rewrite the linear system into the matrix-vector form A = 5 Fuse elementary row operation to solve this linear system. Is the solution use elementary row operation to find the inverse of A and then solve the linear system. Verify the solution is the same as (b). give the null space of matrix A and find the dimension of null space. give the column space of matrix A and find the dimension of the column space of A (Hint: use Rank-Nullity Theorem).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Inner Product Spaces; Author: Jeff Suzuki: The Random Professor;https://www.youtube.com/watch?v=JzCZUx9ZTe8;License: Standard YouTube License, CC-BY