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Note: To enter a matrix, click inside the answer box and choose the "matrix" tab to set up the matrix with the correct dimensions. A) [[0,-2],[3,1],[1,-1]]*[[3,5,-4,1],[-2,-3,0,0]]= ◻ B) [[3,5,-4,1],[-2,-3,0,0]]*[[0,-2],[3,1],[1,-1]]= ◻

Note: To enter a matrix, click inside the answer box and choose the

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Q. Note: To enter a matrix, click inside the answer box and choose the
  1. Identify dimensions: Identify the dimensions of the matrices. Matrix A: 3×23 \times 2 Matrix B: 2×42 \times 4
  2. Check compatibility: Check if the matrices can be multiplied. Matrix A (3×2)(3 \times 2) and Matrix B (2×4)(2 \times 4) can be multiplied because the number of columns in A is equal to the number of rows in B.
  3. Set up multiplication: Set up the multiplication.\newlineMatrix A:\newline[0amp;−23amp;11amp;−1] \begin{bmatrix} 0 & -2 \\ 3 & 1 \\ 1 & -1 \end{bmatrix} \newlineMatrix B:\newline[3amp;5amp;−4amp;1−2amp;−3amp;0amp;0] \begin{bmatrix} 3 & 5 & -4 & 1 \\ -2 & -3 & 0 & 0 \end{bmatrix}
  4. Calculate first row: Calculate the first row of the product matrix.\newline[0amp;−2]×[3amp;5amp;−4amp;1−2amp;−3amp;0amp;0]=[(0∗3+−2∗−2)amp;(0∗5+−2∗−3)amp;(0∗−4+−2∗0)amp;(0∗1+−2∗0)]=[4amp;6amp;0amp;0] \begin{bmatrix} 0 & -2 \end{bmatrix} \times \begin{bmatrix} 3 & 5 & -4 & 1 \\ -2 & -3 & 0 & 0 \end{bmatrix} = \begin{bmatrix} (0*3 + -2*-2) & (0*5 + -2*-3) & (0*-4 + -2*0) & (0*1 + -2*0) \end{bmatrix} = \begin{bmatrix} 4 & 6 & 0 & 0 \end{bmatrix}
  5. Calculate second row: Calculate the second row of the product matrix.\newline[3amp;1]×[3amp;5amp;−4amp;1−2amp;−3amp;0amp;0]=[(3∗3+1∗−2)amp;(3∗5+1∗−3)amp;(3∗−4+1∗0)amp;(3∗1+1∗0)]=[7amp;12amp;−12amp;3] \begin{bmatrix} 3 & 1 \end{bmatrix} \times \begin{bmatrix} 3 & 5 & -4 & 1 \\ -2 & -3 & 0 & 0 \end{bmatrix} = \begin{bmatrix} (3*3 + 1*-2) & (3*5 + 1*-3) & (3*-4 + 1*0) & (3*1 + 1*0) \end{bmatrix} = \begin{bmatrix} 7 & 12 & -12 & 3 \end{bmatrix}
  6. Calculate third row: Calculate the third row of the product matrix.\newline[1amp;−1]×[3amp;5amp;−4amp;1−2amp;−3amp;0amp;0]=[(1∗3+−1∗−2)amp;(1∗5+−1∗−3)amp;(1∗−4+−1∗0)amp;(1∗1+−1∗0)]=[5amp;8amp;−4amp;1] \begin{bmatrix} 1 & -1 \end{bmatrix} \times \begin{bmatrix} 3 & 5 & -4 & 1 \\ -2 & -3 & 0 & 0 \end{bmatrix} = \begin{bmatrix} (1*3 + -1*-2) & (1*5 + -1*-3) & (1*-4 + -1*0) & (1*1 + -1*0) \end{bmatrix} = \begin{bmatrix} 5 & 8 & -4 & 1 \end{bmatrix}
  7. Combine rows: Combine the rows to form the final product matrix.\newline[4amp;6amp;0amp;07amp;12amp;−12amp;35amp;8amp;−4amp;1] \begin{bmatrix} 4 & 6 & 0 & 0 \\ 7 & 12 & -12 & 3 \\ 5 & 8 & -4 & 1 \end{bmatrix}

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