E=[[0,3,5],[5,5,2]] and D=[[3,4],[3,-2],[4,-2]] Let H=ED. Find H. H=

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E=[[0,3,5],[5,5,2]] and  D=[[3,4],[3,-2],[4,-2]] Let  H=ED. Find  H.  H=

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Understand matrix multiplication: Understand matrix multiplication. 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 E is a 2x3 matrix and matrix D is a 3x2 matrix, so they can be multiplied to result in a 2x2 matrix H.Set up the multiplication: Set up the multiplication. We will calculate each element of matrix H by taking the dot product of the corresponding row from matrix E and the corresponding column from matrix D.Calculate first element of H: Calculate the first element of matrix H (H[1,1]). H[1,1] = E[1,1]*D[1,1] + E[1,2]*D[2,1] + E[1,3]*D[3,1] H[1,1] = 0*3 + 3*3 + 5*4 H[1,1] = 0 + 9 + 20 H[1,1] = 29Calculate second element of H: Calculate the second element of matrix H (H[1,2]). H[1,2] = E[1,1]*D[1,2] + E[1,2]*D[2,2] + E[1,3]*D[3,2] H[1,2] = 0*4 + 3*(-2) + 5*(-2) H[1,2] = 0 - 6 - 10 H[1,2] = -16Calculate third element of H: Calculate the third element of matrix H (H[2,1]). H[2,1] = E[2,1]*D[1,1] + E[2,2]*D[2,1] + E[2,3]*D[3,1] H[2,1] = 5*3 + 5*3 + 2*4 H[2,1] = 15 + 15 + 8 H[2,1] = 38Calculate fourth element of H: Calculate the fourth element of matrix H (H[2,2]). H[2,2] = E[2,1]*D[1,2] + E[2,2]*D[2,2] + E[2,3]*D[3,2] H[2,2] = 5*4 + 5*(-2) + 2*(-2) H[2,2] = 20 - 10 - 4 H[2,2] = 6Combine elements for matrix H: Combine the elements to form matrix H. H = [[H[1,1], H[1,2]],      [H[2,1], H[2,2]]] H = [[29, -16],      [38, 6]]

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

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