F1.4 Question 5,6,7,8 ### Exercise Set 1.4**In Exercises 1–2, verify that the following matrices and scalars satisfy the stated properties of Theorem 1.4.1.**Given matrices:\[ A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}, B = \begin{bmatrix} 0 & 2 \\ 1 & -4 \end{bmatrix}, C = \begin{bmatrix} 4 & 1 \\ -3 & -2 \end{bmatrix} \]Scalars: \(a = 4, \quad b = -7\)1. **Verify the following properties:** - **(a)** The associative law for matrix addition. - **(b)** The associative law for matrix multiplication. - **(c)** The left distributive law. - **(d)** \(a(b + c) = aC + bC\).2. **Verify the following properties:** - **(a)** \(\alpha(BC) = (aB)C = B(aC)\). - **(b)** \(A(B - C) = AB - AC\). - **(c)** \((B + C)A = BA + CA\). - **(d)** \(a(bC) = (ab)C\).**In Exercises 3–4, verify that the matrices and scalars in Exercise 1 satisfy the stated properties.**3. **Verify the following properties:** - **(a)** \((A^T)^T = A\). - **(b)** \((AB)^T = B^TA^T\).4. **Verify the following properties:** - **(a)** \((A + B)^T = A^T + B^T\). - **(b)** \((aC)^T = aC^T\).**In Exercises 5–8, use Theorem 1.4.5 to compute the inverse of the given matrix.**5. Given matrix:\[ A = \begin{bmatrix} 2 & -3 \\ 4 & 4 \end{bmatrix} \]6. Given matrix:

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Answered: 5. A = - 12 -3 4 [2 0 0 3 7. C C= 6. B…

5. A = - 12 -3 4 [2 0 0 3 7. C C= 6. B = 3 5 2 6 D = [-2 -1 8. D=

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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