1M2be a vector in the vector space V of 2 × 2 matrices with real number entries. Let0.10.be an ordered basis for V.a. Write M as a linear combination of elements of C.[1 -6'0 10.2 -711b. Let [M]c denote the coordinate representation of M relative to the basis C. Find thecoordinate vector representation for M relative to the basis C. Your answer should be avector of the general form <1,2,3,4>.[M]c

The given matrix is M=1-62-7 The basis of the vector space V are C=1001,0110,100-1,0-110

M be a vector in the vector space V of 2 × 2 matrices with real number entries. Let 0. be an ordered basis for V. a. Write M as a linear combination of elements of C. -6 0 1 0 -1 2 -7 1 b. Let [M]c denote the coordinate representation of M relative to the basis C. Find the coordinate vector representation for M relative to the basis C. Your answer should be a vector of the general form <1,2,3,4>. [M]c = %3D

M be a vector in the vector space V of 2 × 2 matrices with real number entries. Let 0. be an ordered basis for V. a. Write M as a linear combination of elements of C. -6 0 1 0 -1 2 -7 1 b. Let [M]c denote the coordinate representation of M relative to the basis C. Find the coordinate vector representation for M relative to the basis C. Your answer should be a vector of the general form <1,2,3,4>. [M]c = %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: In P2, find the the standard basis C = {1,t,t²}. Then find the B-coordinate vector for − 4 + 10t −…

A: We know that is a vector space consisting of the set of all the polynomials of degree lessthan or…

Q: Give an example of a set of nonzero vectors in R3 that generates R3 but is not a basis for R3.…

A: Definition 1 : A basis β for a vector space V is a linearly independent subset of V that generates…

Q: Find all values of h so that the set of vectors 4 forms a basis for R3? Justify your answer.

Q: Find the value of the vector product XY using the matrices below where p = 9 and q = 6: X = p -1 q…

Q: Find the coordinate vector of x2 + x - 17 relative to the basis {x² + 1, x + 2, x - 3}.

Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors: (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: Let A= {a,,a2,a3} and B= {b,.b2.b3} be bases for a vector space V, and suppose b, = 5a, - 3a3, b2 =…

Q: https://www.youtube.com/watch?v=pE5yxgmXMmQ&t=267s This video was given as a guide

A: ANSWER AND SOLUTION: To find the coordinate vector of the polynomial f(x) = −8x3 + 3x2 − 3x + 7…

Q: Describe the additive inverse of a vector in the vector space.R3

Q: In P,, find the change-of-coordinates matrix from the basis B= (1-2t+P,3-5t+41,1 B-coordinate vector…

A: Given B=1-2t+t2, 3-5t+4t2, 1+4t2. To find P2 that transforms B to C, where C=1,t,t2 PC←B=131-2-50144…

Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

Q: Find the vector x determined by the coordinate vector ---(DBE) 8 and the basis B = 0 XB = The vector…

Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. - 1 2 - 4 B=…

A: The vector x is the linear combination of the vector in basis B.

Q: Determine the orthogonal basis by calculating w1 = w2 - [(23,5)] - [(-9,-2)] and calculating w2 Now…

Q: -9 -10 12 -15 A = 4 -8 6 6 0 9

Q: Express v = (-i, 2 + i, -1) as a linear combination of the following basis vectors given below.…

A: According to the given information it is required to express the given vector v as a linear…

Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: Find a basis B for the span of the given vectors. -H H. B= 11

Q: In P,, find the change-of-coordinates matrix from the basis B = {1+3r²,2+t+7t?,1- 41} to the…

A: Given that B={1+3t2,2+t+7t2,1-4t} is a basis for ℙ2. To find the change of…

Q: Oa + Ob+0c + 4d la + (-1) b+ (-2) c +4d Oa + 1b + (-2) c + 5d la + (-1) b+ (-2) c + 2d 2a + 1b+…

A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d To Find:…

Q: nd a basis for the set of all vectors of the form below, where a, b, c are real numbers. [ a-2b+5c,…

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

1
M
2
be a vector in the vector space V of 2 × 2 matrices with real number entries. Let
0.
1
0.
be an ordered basis for V.
a. Write M as a linear combination of elements of C.
[1 -6'
0 1
0.
2 -7
1
1
b. Let [M]c denote the coordinate representation of M relative to the basis C. Find the
coordinate vector representation for M relative to the basis C. Your answer should be a
vector of the general form <1,2,3,4>.
[M]c

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Nacho claims that every vector in R³ (vector in 3 dimensions) can be written as a combination of a1, a2, a3. Is he correct? yes/no and why? Mickey Rats claims that any set of linear independent vectors must be a Basis. Is he correct? Explain.
Pick every true statement which applies to the following set of vectors. {8·4)} O This set spans R^3 O Every vector in its span can be written uniquely as a linear combination of these vectors O This set of vectors is linearly dependent O This set is a basis of R^3 O None of the above answers are true
Determine whether or not the given vectors in Rn form a basisfor Rna. v1 = (2, 0, 0, 0), v2 = (0, 7, 0, 0), v3 = (0, 0, 4, 6), v4 = (0, 0, 4, 2)b. v1 = (1, 7, −4), v2 = (3, 2, 5), v3 = (6, 5, 1), v4 = (0, 7, 4)
Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the standard basis vectors in R3. (c) Find -3u.
Let u = [1, -6, 3] and v= [-3, 3, 017. Find the vector w = 3u2v and its additive inverse. W= W = 1. 00% II
Consider the following matrix: 1 -2 3 0 −3 A-3 6 -9 09 -2 5-9 -2 9 Give a basis for each of im(A) and null(A). Number of Vectors: 1 {} Basis for im(A) Number of Vectors: 1 {} Basis for null(A) 0
Help neeee in part a and B thanks in advance
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. 0 --[142-9] A = -5 A nonzero vector in Nul A is (Type an integer or decimal for each matrix element.) A nonzero vector in Col A is. (Type an integer or decimal for each matrix element.)
Let A= {a;.a2,a3} and B = {b,.b2.b3} be bases for a vector space V, and suppose a, = 5b, - – 2b3. a. Find the change-of-coordinates matrix from A to B. b. Find (xlg for x= 5a, + 6a2 + az. a P B-A b. xlg =0 (Simplify your answer.)
Let A- (a, a2 a3} and B= (b, bz b; be bases for a vector space V, and suppose b, = 2a, - 4az, b,= -a, + 4az, by =a, +az + 3a,. %3D %3D a Find the change of-coordinates matrix from B to A b. Find (x, for x=b, - 2b, + 2b,