Here are the matrices and operations to be evaluated for their definition:Matrix A:\[ A = \begin{bmatrix} -1 & 4 & -1 \end{bmatrix} \]- This is a 1x3 row matrix.Matrix B:\[ B = \begin{bmatrix} -5 & -8 \\ -8 & 0 \end{bmatrix} \]- This is a 2x2 matrix.Matrix C:\[ C = \begin{bmatrix} 3 \\ -1 \\ -6 \\ -6 \end{bmatrix} \]- This is a 4x1 column matrix.**Determine if each of the following operations is defined (answer yes or no):**1. **Addition Operations:** - $ A + B $ - $ A + C $ - $ B + C $2. **Multiplication Operations:** - $ AB $ - $ BA $ - $ AC $ - $ CA $ - $ BC $ - $ CB $To determine if operations are defined, follow these guidelines:- **Addition of Matrices:** Two matrices can be added if they have the same dimensions.- **Multiplication of Matrices:** Matrix multiplication is defined if the number of columns in the first matrix equals the number of rows in the second matrix. **Proceed to evaluate each operation based on these rules.**

(.) Given matrices are, Matrix is of order .Matrix is of order .Matrix is of order .

Answered: en decide if each of the following…

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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Question

Here are the matrices and operations to be evaluated for their definition:

Matrix A:
\[ A = \begin{bmatrix} -1 & 4 & -1 \end{bmatrix} \]
- This is a 1x3 row matrix.

Matrix B:
\[ B = \begin{bmatrix} -5 & -8 \\ -8 & 0 \end{bmatrix} \]
- This is a 2x2 matrix.

Matrix C:
\[ C = \begin{bmatrix} 3 \\ -1 \\ -6 \\ -6 \end{bmatrix} \]
- This is a 4x1 column matrix.

**Determine if each of the following operations is defined (answer yes or no):**

1. **Addition Operations:**
- $ A + B $
- $ A + C $
- $ B + C $

2. **Multiplication Operations:**
- $ AB $
- $ BA $
- $ AC $
- $ CA $
- $ BC $
- $ CB $

To determine if operations are defined, follow these guidelines:

- **Addition of Matrices:** Two matrices can be added if they have the same dimensions.
- **Multiplication of Matrices:** Matrix multiplication is defined if the number of columns in the first matrix equals the number of rows in the second matrix.

**Proceed to evaluate each operation based on these rules.**

Expert Solution

Step 1: We write the given matrices.

(.) Given matrices are,

$A equals left square bracket negative 1 space space 4 space space minus 1 right square bracket space space space comma space space space B equals open square brackets table row cell negative 5 end cell cell negative 8 end cell row cell negative 8 end cell cell space space 0 end cell end table close square brackets space space comma space space c equals open square brackets table row 3 row cell negative 1 end cell row cell negative 6 end cell row cell negative 6 end cell end table close square brackets$

Matrix $A$ is of order $1 cross times 3$ .

Matrix $B space$ is of order $2 cross times 2$ .

Matrix $c$ is of order $4 cross times 1$ .