3524with a linear map f:R² → R² then thecharacteristic equation of the matrixP is:If P=is the matrix associatedA. 72-2²-2=0B. 1212-10-0C. 722-52-2=0D. 2²+72+2=0E. 2²-72-2=0

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Answered: 35 24 with a linear map f:R² → R² then…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Let a € R, and define vectors u₁, U₂, U3 € R³ in terms of a by - 8. a U₁ = 2 U₂ = 3a + 3 2a +3 a² + 3a 7 [4a - 2] 13 = 3a-1 2a² (a) Show that the rank of the matrix [u₁ u₂ u3] does not depend on a. Hint: Find the rank by putting the matrix in row-echelon form. (b) Making reference to a fact from the course, show that u₁, U₂, U3 never span R³, no matter what value a takes. (c) Express u3 as a linear combination of u₁ and u2, i.e., as c₁u₁ + c₂U2. The scalars c₁ and c₂ will depend on a.
Q31.
P = ) Let A = -15 0 24 -8 -8 ❤ -3 0 16 13 Find an invertible matrix P and a diagonal matrix D such that D = P¯¹ AP. D=
4a). The transformation defined by the matrix A = [14 5 stretches images in R² in the directions y = x and y = -x. Figure out the factor by which anything in the y = x direction is stretched and the factor by which anything in the y = -x direction is stretched. 4b). The transformation defined by the matrix B = -82 -55 13 3] stretches images in R2 in one direction by a factor of 3 and some other direction by a factor of 2. Figure out what direction gets stretched by a factor of 3 and what direction gets stretched by a factor of 2. 4c). The transformation defined by the matrix C = stretches images in R2 in two directions. Find the directions and the factors by which it stretches in those directions.
( 8.) Let A be a nonsingular n x n matrix, then there are elementary matrices G1, G2, such that Gg .. G2 G A =1. GR . True / False :
Find the change of basis matrix [B]• 2 -{[0]·[15]} = { [0]·[4]} C 4 B
4. Let -{0-0)-G)} (a) Define an appropriate matrix and apply the rref command to determine if w = 25 55 can be expressed as a linear combination of {V1, V2, V3}. 10 S = {V1, V2, V3} = 3
8 4. a) Given the following matrices A- B= -5 11 9 11 find and C- 6 1, 2 16 i. il. 2A+ A+3B A- B+ C b) Determine which of the matrices A, B and C is/are singular with reasons.
b. Let B = {T1, t2, t3}, C = {71, 72, 73}, be two orthogonal bases for R³. Show that the change-of-coordinates matrix PB>c is orthogonal.
-1 2 1 -2 1 1 1 Let P = and P = B-A -1 -1 -2 2 C-A -1 2 2 4 The change of basis matrix P would be: B-C 1 1 1 -2 -1 2 -1 3 1 -5 1 -3 0 -1 4 4
Let A = 1 -2 5 7 0 1 3 2 3 4 -1 -2 -1 -2 3 5 Find the matrices B = ¹/(A + AT) and C = (A – A¹). What is the relation between A and B + C?

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35 24 with a linear map f:R² → R² then the characteristic equation of the matrix P is: If P= is the matrix associated A. 72-2²-2=0 B. 1212-10-0 C. 722-52-2=0 D. 2²+72+2=0 E. 2²-72-2=0