Elementary Linear Algebra: Applications Version
12th Edition
ISBN: 9781119282365
Author: Howard Anton, Chris Rorres, Anton Kaul
Publisher: WILEY
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4. Solve the system of equations and express your solution using vectors.
2x1 +5x2+x3 + 3x4 = 9
-x2+x3 + x4 = 1
-x1-6x2+3x3 + 2x4
= -1
3. Simplify the matrix expression
A(A-B) - (A+B)B-2(A - B)2 + (A + B) 2
[2 pts] 1. Let A =
[.
1 -1 0
-343
and B =
05
5 -7
304
Compute (7A - 3B) - 4(2A - B).
Chapter 4 Solutions
Elementary Linear Algebra: Applications Version
Ch. 4.1 - Let V be the set of all ordered pairs of real...Ch. 4.1 - Let V be the set of all ordered pairs of real...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - In Exercises 312, determine whether each set...Ch. 4.1 - Verify Axioms 3, 7, 8, and 9 for the vector space...Ch. 4.2 - In Exercises 12, use the Subspace Test to...
Ch. 4.2 - In Exercises 12, use the Subspace Test to...Ch. 4.2 - In Exercises 34, use the Subspace Test to...Ch. 4.2 - In Exercises 56, use the Subspace Test to...Ch. 4.2 - In Exercises 78, use the Subspace Test to...Ch. 4.2 - In Exercises 78, use the Subspace Test to...Ch. 4.2 - In Exercises 1112, use the Subspace Test to...Ch. 4.2 - In Exercises 1112, use the Subspace Test to...Ch. 4.2 - In Exercises 1314, use the Subspace Test to...Ch. 4.2 - In Exercises 1516, use the Subspace Test to...Ch. 4.2 - In parts (a)(h) determine whether the statement is...Ch. 4.3 - Which of the following are linear combinations of...Ch. 4.3 - Express the following as linear combinations of u...Ch. 4.3 - Prove that if {u, v} spans the vector space V,...Ch. 4.4 - Explain why the following form linearly dependent...Ch. 4.4 - In each part, determine whether the vectors are...Ch. 4.4 - In each part, determine whether the vectors are...Ch. 4.4 - In each part, determine whether the vectors are...Ch. 4.4 - In each part, determine whether the matrices are...Ch. 4.4 - a. Show that the three vectors v1 = (0, 3, 1, 1),...Ch. 4.4 - Prove that if {v1, v2} is linearly independent and...Ch. 4.5 - Use the method of Example 3 to show that the...Ch. 4.5 - Use the method of Example 3 to show that the...Ch. 4.5 - Show that the following polynomials form a basis...Ch. 4.5 - Prob. 5ECh. 4.5 - Show that the following matrices form a basis for...Ch. 4.5 - In each part, show that the set of vectors is not...Ch. 4.5 - Show that the following vectors do not form a...Ch. 4.5 - Show that the following matrices do not form a...Ch. 4.5 - Find the coordinate vector of w relative to the...Ch. 4.5 - Find the coordinate vector of v relative to the...Ch. 4.5 - Find the coordinate vector of p relative to the...Ch. 4.5 - In Exercises 1516, first show that the set S =...Ch. 4.5 - In Exercises 1718, first show that the set S =...Ch. 4.5 - In words, explain why the sets of vectors in parts...Ch. 4.5 - In any vector space a set that contains the zero...Ch. 4.5 - The accompanying figure shows a rectangular...Ch. 4.5 - The accompanying figure shows a rectangular...Ch. 4.5 - Consider the coordinate vectors...Ch. 4.5 - The basis that we gave for M22 in Example 4...Ch. 4.5 - Prove that if V is a subspace of a vector space W...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.5 - In parts (a)(e) determine whether the statement is...Ch. 4.6 - In Exercises 16, find a basis for the solution...Ch. 4.6 - In Exercises 16, find a basis for the solution...Ch. 4.6 - In Exercises 16, find a basis for the solution...Ch. 4.6 - In each part, find a basis for the given subspace...Ch. 4.6 - Find the dimension of each of the following vector...Ch. 4.6 - a. Show that the set W of all polynomials in P2...Ch. 4.6 - Find a standard basis vector for R3 that can be...Ch. 4.6 - Let {v1, v2, v3} be a basis for a vector space V....Ch. 4.6 - The vectors v1 = (1, 0, 0, 0) and v2 = (1, 1, 0,...Ch. 4.6 - Find a basis for the subspace of R4 that is...Ch. 4.6 - Let S be a basis for an n-dimensional vector space...Ch. 4.6 - Let S = {v1, v2,, vr} be a nonempty set of vectors...Ch. 4.6 - State the two parts of Theorem 4.6.2 in...Ch. 4.6 - In each part, let S be the standard basis for P2....Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.6 - In parts (a)(k) determine whether the statement is...Ch. 4.8 - In Exercises 34, determine whether b is in the...Ch. 4.8 - In Exercises 78, find the vector form of the...Ch. 4.8 - In Exercises 910, find bases for the null space...Ch. 4.8 - In Exercises 1112, a matrix in row echelon form is...Ch. 4.8 - In Exercises 1415, find a basis for the subspace...
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- 20 2. Let A = = [ -2 0 1 3 ] and B = 2 3 -1 2 For each of the following, calculate the product or indicate why it is undefined: (a) AB (b) BAarrow_forwardAnswer the number questions with the following answers +/- 2 sqrt(2) +/- i sqrt(6) (-3 +/-3 i sqrt(3))/4 +/-1 +/- sqrt(6) +/- 2/3 sqrt(3) 4 -3 +/- 3 i sqrt(3)arrow_forward1 Matching 10 points Factor and Solve 1)x3-216 0, x = {6,[B]} 2) 16x3 = 54 x-[3/2,[D]] 3)x4x2-42 0 x= [ +/-isqrt(7), [F] } 4)x+3-13-9x x=[+/-1.[H]] 5)x38x2+16x=0, x = {0,[K}} 6) 2x6-10x-48x2-0 x-[0, [M], +/-isqrt(3)) 7) 3x+2x²-8 x = {+/-i sqrt(2), {Q}} 8) 5x³-3x²+32x=2x+18 x = {3/5, [S]} [B] [D] [F] [H] [K] [M] [Q] +/-2 sqrt(2) +/- i sqrt(6) (-3+/-3 i sqrt(3))/4 +/- 1 +/-sqrt(6) +/- 2/3 sqrt(3) 4 -3 +/- 3 i sqrt(3) [S]arrow_forward
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