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(6) Let A be a nxn matrix. If N(A) = {0}, then then system Ax = b has a unique solution for a given vector bЄ Rn. 1 (7) The following vectors 66 16 142 1 are linearly independent in -2 the vector space M2×2. (8) Let A be a 4×5 matrix. If a₁, a2 and a are linearly independent and a3 = a₁ + 2a2, a5 = 2a1 + a2 +3a4, the row echelon form (REF) of A is 1 0 1 0 21 0 1 20 1 0 LO 00 1 0 0 0 1 3. (9) The following transformation L: R³ R³ defined by L(x) 1+ X1 = x1 + x2 Lx₁ - 2x3] is a linear transformation. (10) Let L₁: R² → R² be the reflection about the x-axis, and L2: R² rotation counterclockwise with the angle 0, then R² be the L2° L₁ = L1 L2. 0

(6) Let A be a nxn matrix. If N(A) = {0}, then then system Ax = b has a unique solution for a given vector bЄ Rn. 1 (7) The following vectors 66 16 142 1 are linearly independent in -2 the vector space M2×2. (8) Let A be a 4×5 matrix. If a₁, a2 and a are linearly independent and a3 = a₁ + 2a2, a5 = 2a1 + a2 +3a4, the row echelon form (REF) of A is 1 0 1 0 21 0 1 20 1 0 LO 00 1 0 0 0 1 3. (9) The following transformation L: R³ R³ defined by L(x) 1+ X1 = x1 + x2 Lx₁ - 2x3] is a linear transformation. (10) Let L₁: R² → R² be the reflection about the x-axis, and L2: R² rotation counterclockwise with the angle 0, then R² be the L2° L₁ = L1 L2. 0

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.1: Operations With Matrices
Problem 72E: Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
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Determine whether it's true or false and the reasoning is needed

(6) Let A be a nxn matrix. If N(A) = {0}, then then system Ax = b has a unique solution for a given vector bЄ Rn. 1 (7) The following vectors 66 16 142 1 are linearly independent in -2 the vector space M2×2. (8) Let A be a 4×5 matrix. If a₁, a2 and a are linearly independent and a3 = a₁ + 2a2, a5 = 2a1 + a2 +3a4, the row echelon form (REF) of A is 1 0 1 0 21 0 1 20 1 0 LO 00 1 0 0 0 1 3.
Transcribed Image Text:(6) Let A be a nxn matrix. If N(A) = {0}, then then system Ax = b has a unique solution for a given vector bЄ Rn. 1 (7) The following vectors 66 16 142 1 are linearly independent in -2 the vector space M2×2. (8) Let A be a 4×5 matrix. If a₁, a2 and a are linearly independent and a3 = a₁ + 2a2, a5 = 2a1 + a2 +3a4, the row echelon form (REF) of A is 1 0 1 0 21 0 1 20 1 0 LO 00 1 0 0 0 1 3.
(9) The following transformation L: R³ R³ defined by L(x) 1+ X1 = x1 + x2 Lx₁ - 2x3] is a linear transformation. (10) Let L₁: R² → R² be the reflection about the x-axis, and L2: R² rotation counterclockwise with the angle 0, then R² be the L2° L₁ = L1 L2. 0
Transcribed Image Text:(9) The following transformation L: R³ R³ defined by L(x) 1+ X1 = x1 + x2 Lx₁ - 2x3] is a linear transformation. (10) Let L₁: R² → R² be the reflection about the x-axis, and L2: R² rotation counterclockwise with the angle 0, then R² be the L2° L₁ = L1 L2. 0
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