F=[[2,3],[0,5],[-1,-1]] and D=[[-1,0],[4,2]] Let H=FD. Find H. H=

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F=[[2,3],[0,5],[-1,-1]] and  D=[[-1,0],[4,2]] Let  H=FD. Find  H.  H=

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Understand matrix multiplication rules: Understand matrix multiplication rules. To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.Verify matrix multiplication for F and D: Verify if the matrices F and D can be multiplied. Matrix F has dimensions 3x2 (3 rows and 2 columns), and matrix D has dimensions 2x2 (2 rows and 2 columns). Since the number of columns in F is equal to the number of rows in D, we can multiply F by D.Set up matrix multiplication for F and D: Set up the multiplication of matrices F and D. To multiply F by D, we will take the dot product of the rows of F with the columns of D. This will give us a new matrix H with dimensions 3x2.Calculate first element of matrix H: Calculate the first element of matrix H. Multiply the first row of F by the first column of D: H[1,1] = (2 * -1) + (3 * 4) = -2 + 12 = 10Calculate second element of first row of H: Calculate the second element of the first row of matrix H. Multiply the first row of F by the second column of D: H[1,2] = (2 * 0) + (3 * 2) = 0 + 6 = 6Calculate first element of second row of H: Calculate the first element of the second row of matrix H. Multiply the second row of F by the first column of D: H[2,1] = (0 * -1) + (5 * 4) = 0 + 20 = 20Calculate second element of second row of H: Calculate the second element of the second row of matrix H. Multiply the second row of F by the second column of D: H[2,2] = (0 * 0) + (5 * 2) = 0 + 10 = 10Calculate first element of third row of H: Calculate the first element of the third row of matrix H. Multiply the third row of F by the first column of D: H[3,1] = (-1 * -1) + (-1 * 4) = 1 - 4 = -3Calculate second element of third row of H: Calculate the second element of the third row of matrix H. Multiply the third row of F by the second column of D: H[3,2] = (-1 * 0) + (-1 * 2) = 0 - 2 = -2Combine elements to form matrix H: Combine all the elements to form matrix H. H = [[10, 6], [20, 10], [-3, -2]]

$F=\left[\begin{array}{rr}2 & 3 \\ 0 & 5 \\ -1 & -1\end{array}\right]$ and $\mathrm{D}=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{FD}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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