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e. 2-1 C 1 1 0-1 2 с Exercise 3.2.3 Let A, B, an and assume that det A = -1,

e. 2-1 C 1 1 0-1 2 с Exercise 3.2.3 Let A, B, an and assume that det A = -1,

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.4: Transistion Matrices And Similarity
Problem 17E
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Please answer Exercise 3.3.2 e).
ing matrices. a. a. C. e. 5 1 3 1 -1 2 ⠀ ⠀⠀ [ -1 2 3 3 10 14 8 0 1 03 3-4 c 58 132 2 C 10 02 c -1 C 5 1 0-1 2 C 2-1 с 1 b. b. d. f. 0 с -1 2 C -C 4 C 3 c 2 c 5 C 4 1 c 1 01 C -1 1 C Exercise 3.2.3 Let A, B, and C denote nx n matrices and assume that det A = -1, det B = 2, and det C = 3. Evaluate: C. -1 a. 1 0-1 Exercise 3.2.2 Use determinants to find which real val- ues of c make each of the following matrices invertible. 3.2. Determinants and Matrix Inverses 167 Exercise 3.2.8 Solve each of the following by Cramer's rule: 2x + y = 1 3x + 7y=-2 5x+y z=-7 c. 2x-y-2z = 6 +2z=-7 3x d. a. A = 2 2-1 2 2-1 2 3 2 1 112 -1 2 1 b. 3x+4y= 9 2x - y = -1 Exercise 3.2.9 Use Theorem 3.2.4 to find the (2, 3)- entry of A-¹ if: 1 4x y + 3z d. 6x+2y- z = 0 3x+3y + 2z=-1 b. A = 12 -1 1 3 1 04 7
Transcribed Image Text:ing matrices. a. a. C. e. 5 1 3 1 -1 2 ⠀ ⠀⠀ [ -1 2 3 3 10 14 8 0 1 03 3-4 c 58 132 2 C 10 02 c -1 C 5 1 0-1 2 C 2-1 с 1 b. b. d. f. 0 с -1 2 C -C 4 C 3 c 2 c 5 C 4 1 c 1 01 C -1 1 C Exercise 3.2.3 Let A, B, and C denote nx n matrices and assume that det A = -1, det B = 2, and det C = 3. Evaluate: C. -1 a. 1 0-1 Exercise 3.2.2 Use determinants to find which real val- ues of c make each of the following matrices invertible. 3.2. Determinants and Matrix Inverses 167 Exercise 3.2.8 Solve each of the following by Cramer's rule: 2x + y = 1 3x + 7y=-2 5x+y z=-7 c. 2x-y-2z = 6 +2z=-7 3x d. a. A = 2 2-1 2 2-1 2 3 2 1 112 -1 2 1 b. 3x+4y= 9 2x - y = -1 Exercise 3.2.9 Use Theorem 3.2.4 to find the (2, 3)- entry of A-¹ if: 1 4x y + 3z d. 6x+2y- z = 0 3x+3y + 2z=-1 b. A = 12 -1 1 3 1 04 7
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