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Q-2: [1 2 1] a) Let E = |0 1 3. Find all values of r for which E has inverse. Find, if 1 0 rl possible, E¬1 for r = -1. b) Let A = 8 8 1. Find all possible 2 x 2 matrices B such that AB = 02. Lo

Q-2: [1 2 1] a) Let E = |0 1 3. Find all values of r for which E has inverse. Find, if 1 0 rl possible, E¬1 for r = -1. b) Let A = 8 8 1. Find all possible 2 x 2 matrices B such that AB = 02. Lo

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 5AEXP
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1. Q-1: Answer each of the following as True or False justifying your answers: 100 a) If A =; then A100 = (-)*"G b) For any three matrices A, B and C, if AB = BA and BC = CB, then AC = CA. 1 [0 c) If (I – 24")-1 = then A = I d) If A and B are 4 x 4 nonsingular matrices such that |2A-'B²| = 32, then |A| = B. e) Let S %3D {(1,0,0,0), (01,0,0), (2,3,5а,0), (а, 0,2, а — R*. The set S is linearly independent if and only if a + 0. 2)} be set of vectors in 2. Q-2: [1 a) Let E = |0 li possible, E-1 for r = -1. 2 11 1 3. Find all values of r for which E has inverse. Find, if rl b) Let A = . Find all possible 2 × 2 matrices B such that AB = 02. 3. Q-3: X, + 2хz — хз — 2х, — 2 a) Find the solution set of the linear system:{2x1 + x2 – 2x3 + 2x4 = 1. (x; + 2xz + 3хз + 2x, 3D 6 b) Let A = Evaluate |A|. 4. Q-4: a) Determine whether the vector (9,0,9) is a linear combination of the vectors (1,1,0), (1,0,1), (2,1,1) and (0,1, -1). b) Determine whether the vectors (0,3, –1,2), (1,2,1, –2) and (3,0,5, –10) in R* are linearly independent.
Transcribed Image Text:1. Q-1: Answer each of the following as True or False justifying your answers: 100 a) If A =; then A100 = (-)*"G b) For any three matrices A, B and C, if AB = BA and BC = CB, then AC = CA. 1 [0 c) If (I – 24")-1 = then A = I d) If A and B are 4 x 4 nonsingular matrices such that |2A-'B²| = 32, then |A| = B. e) Let S %3D {(1,0,0,0), (01,0,0), (2,3,5а,0), (а, 0,2, а — R*. The set S is linearly independent if and only if a + 0. 2)} be set of vectors in 2. Q-2: [1 a) Let E = |0 li possible, E-1 for r = -1. 2 11 1 3. Find all values of r for which E has inverse. Find, if rl b) Let A = . Find all possible 2 × 2 matrices B such that AB = 02. 3. Q-3: X, + 2хz — хз — 2х, — 2 a) Find the solution set of the linear system:{2x1 + x2 – 2x3 + 2x4 = 1. (x; + 2xz + 3хз + 2x, 3D 6 b) Let A = Evaluate |A|. 4. Q-4: a) Determine whether the vector (9,0,9) is a linear combination of the vectors (1,1,0), (1,0,1), (2,1,1) and (0,1, -1). b) Determine whether the vectors (0,3, –1,2), (1,2,1, –2) and (3,0,5, –10) in R* are linearly independent.
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