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3. Let A = 20 A AB 9. (a) Find, (b) Find, (c) Find, 730

3. Let A = 20 A AB 9. (a) Find, (b) Find, (c) Find, 730

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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**Matrices and Vector Operations** **3. Consider the following matrices and vector:** - Matrix \( A = \begin{bmatrix} 1 & 5 \\ 1 & 0 \end{bmatrix} \) - Matrix \( B = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) - Matrix \( C = \begin{bmatrix} 1 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix} \) - Vector \( \vec{d} = \begin{bmatrix} 2 \\ 4 \\ 5 \end{bmatrix} \) **Tasks:** (a) Calculate, if possible, the products: \( AB \), \( BA \), \( AC \), \( CA \). (b) Calculate, if possible, the products: \( CC^t \), \( C^t C \), \( \vec{d}^t \vec{d} \), \( \vec{d}\vec{d}^t \). (c) Calculate, if possible, the powers and products: \( A^2 \), \( B^2 \), \( C^2 \), \( (\vec{d})^2 \) where \( A^2 \) is the notation for \( AA \).
Transcribed Image Text:**Matrices and Vector Operations** **3. Consider the following matrices and vector:** - Matrix \( A = \begin{bmatrix} 1 & 5 \\ 1 & 0 \end{bmatrix} \) - Matrix \( B = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) - Matrix \( C = \begin{bmatrix} 1 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix} \) - Vector \( \vec{d} = \begin{bmatrix} 2 \\ 4 \\ 5 \end{bmatrix} \) **Tasks:** (a) Calculate, if possible, the products: \( AB \), \( BA \), \( AC \), \( CA \). (b) Calculate, if possible, the products: \( CC^t \), \( C^t C \), \( \vec{d}^t \vec{d} \), \( \vec{d}\vec{d}^t \). (c) Calculate, if possible, the powers and products: \( A^2 \), \( B^2 \), \( C^2 \), \( (\vec{d})^2 \) where \( A^2 \) is the notation for \( AA \).
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