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1 -1 0 1. Let A=(23¹), B(4). 3 -5 (a) Compute AB and BA. (b) Compute A + B and B + A. (c) If c = 3, show that c(A + B) = cA + cb. (d) Show that (AB)C = A(BC). (e) Compute A²C. (f) Compute B +0. (g) Compute A02x2 and 02x2A, where 02x2 is the 2 × 2 zero matrix. (h) Compute 0A, where 0 is the real number (scalar) zero. (i) Let c = 2 and d = 3. Show that (c+d) A = cA + d.A. = 0 2 = ( ² and C= ² -1 1 3 -2 2

1 -1 0 1. Let A=(23¹), B(4). 3 -5 (a) Compute AB and BA. (b) Compute A + B and B + A. (c) If c = 3, show that c(A + B) = cA + cb. (d) Show that (AB)C = A(BC). (e) Compute A²C. (f) Compute B +0. (g) Compute A02x2 and 02x2A, where 02x2 is the 2 × 2 zero matrix. (h) Compute 0A, where 0 is the real number (scalar) zero. (i) Let c = 2 and d = 3. Show that (c+d) A = cA + d.A. = 0 2 = ( ² and C= ² -1 1 3 -2 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Let \( A = \begin{pmatrix} 1 & -1 \\ 2 & 3 \end{pmatrix} \), \( B = \begin{pmatrix} 0 & 1 \\ 3 & -5 \end{pmatrix} \), and \( C = \begin{pmatrix} 0 & 1 \\ 3 & -2 \end{pmatrix} \). (a) Compute \( AB \) and \( BA \). (b) Compute \( A + B \) and \( B + A \). (c) If \( c = 3 \), show that \( c(A + B) = cA + cB \). (d) Show that \( (AB)C = A(BC) \). (e) Compute \( A^2C \). (f) Compute \( B + 0 \). (g) Compute \( A0_{2 \times 2} \) and \( 0_{2 \times 2}A \), where \( 0_{2 \times 2} \) is the \( 2 \times 2 \) zero matrix. (h) Compute \( 0A \), where \( 0 \) is the real number (scalar) zero. (i) Let \( c = 2 \) and \( d = 3 \). Show that \( (c + d)A = cA + dA \).
Transcribed Image Text:1. Let \( A = \begin{pmatrix} 1 & -1 \\ 2 & 3 \end{pmatrix} \), \( B = \begin{pmatrix} 0 & 1 \\ 3 & -5 \end{pmatrix} \), and \( C = \begin{pmatrix} 0 & 1 \\ 3 & -2 \end{pmatrix} \). (a) Compute \( AB \) and \( BA \). (b) Compute \( A + B \) and \( B + A \). (c) If \( c = 3 \), show that \( c(A + B) = cA + cB \). (d) Show that \( (AB)C = A(BC) \). (e) Compute \( A^2C \). (f) Compute \( B + 0 \). (g) Compute \( A0_{2 \times 2} \) and \( 0_{2 \times 2}A \), where \( 0_{2 \times 2} \) is the \( 2 \times 2 \) zero matrix. (h) Compute \( 0A \), where \( 0 \) is the real number (scalar) zero. (i) Let \( c = 2 \) and \( d = 3 \). Show that \( (c + d)A = cA + dA \).
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