https://file.aiquickdraw.com/mathbot/file/1726718692806tmvlee70.jpg

Let's break down and solve the matrix operations one by one from the image:

The matrices are:

\[
A = \begin{bmatrix} 2 & -3 \\ -1 & 6 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 1 \\ -5 & 2 \end{bmatrix}, \quad C = \begin{bmatrix} -3 & 5 \\ 4 & -2 \end{bmatrix}
\]

### (i) \( 4A \)
To find \( 4A \), we multiply every element of matrix \( A \) by 4:

\[
4A = 4 \times \begin{bmatrix} 2 & -3 \\ -1 & 6 \end{bmatrix}
= \begin{bmatrix} 4 \times 2 & 4 \times (-3) \\ 4 \times (-1) & 4 \times 6 \end{bmatrix}
= \begin{bmatrix} 8 & -12 \\ -4 & 24 \end{bmatrix}
\]

### (ii) \( A + C \)
To add matrices \( A \) and \( C \), we simply add corresponding elements:

\[
A + C = \begin{bmatrix} 2 & -3 \\ -1 & 6 \end{bmatrix} + \begin{bmatrix} -3 & 5 \\ 4 & -2 \end{bmatrix}
= \begin{bmatrix} 2 + (-3) & -3 + 5 \\ -1 + 4 & 6 + (-2) \end{bmatrix}
= \begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix}
\]

### (iii) \( 3B + 2C \)
For this, we first compute \( 3B \) and \( 2C \), then add them.

\[
3B = 3 \times \begin{bmatrix} 4 & 1 \\ -5 & 2 \end{bmatrix}
= \begin{bmatrix} 12 & 3 \\ -15 & 6 \end{bmatrix}
\]

\[
2C = 2 \times \begin{bmatrix} -3 & 5 \\ 4 & -2 \end{bmatrix}
= \begin{bmatrix} -6 & 10 \\ 8 & -4 \end{bmatrix}
\]

Now, add \( 3B \) and \( 2C \):

\[
3B

Do the following matrix operations WITHOUT USING YOUR CALCULATORS: (i) 4A, (ii) A + C, (iii) 3B + 2C, (iv) 2A - C + 4B where A = [[2, -3], [-1, 6]], B = [[4, 1], [-5, 2]], C = [[-3, 5], [4, -2]]

This page breaks down matrix operations, including scalar multiplication and matrix addition, using matrices A, B, and C. Detailed solutions for 4A, A + C, 3B + 2C, and 2A - C + 4B are provided, explaining key matrix algebra concepts.

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