In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

Guida verificata passo dopo passo

Step 1: Identify the matrices A and B. Matrix A is $ \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix} $ and matrix B is $ \begin{bmatrix} 5 & 9 \\ 0 & 7 \end{bmatrix} $.

Step 2: Multiply matrix A by -3. This means multiplying each element of matrix A by -3, resulting in $ -3A = \begin{bmatrix} -3 \times 4 & -3 \times 1 \\ -3 \times 3 & -3 \times 2 \end{bmatrix} $.

Step 3: Multiply matrix B by 2. This means multiplying each element of matrix B by 2, resulting in $ 2B = \begin{bmatrix} 2 \times 5 & 2 \times 9 \\ 2 \times 0 & 2 \times 7 \end{bmatrix} $.

Step 4: Add the resulting matrices from Step 2 and Step 3 element-wise. That is, add corresponding elements from $ -3A $ and $ 2B $ to get $ -3A + 2B = \begin{bmatrix} (-3 \times 4) + (2 \times 5) & (-3 \times 1) + (2 \times 9) \\ (-3 \times 3) + (2 \times 0) & (-3 \times 2) + (2 \times 7) \end{bmatrix} $.

Step 5: Write the resulting matrix from Step 4 as the final answer for $ -3A + 2B $.

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