C=[[1,4],[4,-1],[3,-2]] and D=[[-2,2],[3,0]] Let H=CD. Find H. H=

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C=[[1,4],[4,-1],[3,-2]] and  D=[[-2,2],[3,0]] Let  H=CD. 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. Matrix C is a 3x2 matrix and matrix D is a 2x2 matrix. Since the number of columns in C (which is 2) is equal to the number of rows in D (which is 2), we can multiply these matrices.Set up the multiplication: Set up the multiplication. We will calculate the elements of matrix H by taking the dot product of the rows of matrix C with the columns of matrix D. The resulting matrix H will have the same number of rows as matrix C and the same number of columns as matrix D, so H will be a 3x2 matrix.Calculate first element of H: Calculate the first element of matrix H. The first element of matrix H (H[1,1]) is the dot product of the first row of C and the first column of D. H[1,1] = (1)(-2) + (4)(3) H[1,1] = -2 + 12 H[1,1] = 10Calculate second element of first row: Calculate the second element of the first row of matrix H. The second element of the first row of matrix H (H[1,2]) is the dot product of the first row of C and the second column of D. H[1,2] = (1)(2) + (4)(0) H[1,2] = 2 + 0 H[1,2] = 2Calculate first element of second row: Calculate the first element of the second row of matrix H. The first element of the second row of matrix H (H[2,1]) is the dot product of the second row of C and the first column of D. H[2,1] = (4)(-2) + (-1)(3) H[2,1] = -8 - 3 H[2,1] = -11Calculate second element of second row: Calculate the second element of the second row of matrix H. The second element of the second row of matrix H (H[2,2]) is the dot product of the second row of C and the second column of D. H[2,2] = (4)(2) + (-1)(0) H[2,2] = 8 + 0 H[2,2] = 8Calculate first element of third row: Calculate the first element of the third row of matrix H. The first element of the third row of matrix H (H[3,1]) is the dot product of the third row of C and the first column of D. H[3,1] = (3)(-2) + (-2)(3) H[3,1] = -6 - 6 H[3,1] = -12Calculate second element of third row: Calculate the second element of the third row of matrix H. The second element of the third row of matrix H (H[3,2]) is the dot product of the third row of C and the second column of D. H[3,2] = (3)(2) + (-2)(0) H[3,2] = 6 + 0 H[3,2] = 6

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

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