{:[F=[[1,2],[-2,3]]" and "],[E=[[0,-1,5],[3,2,1]]]:} Let H=FE. Find H. H=

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{:[F=[[1,2],[-2,3]]" and "],[E=[[0,-1,5],[3,2,1]]]:} Let  H=FE. Find  H.  H=

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Matrix Multiplication: To find the matrix H which is the product of matrices F and E, we need to perform matrix multiplication. The matrix F is a 2x2 matrix and the matrix E is a 2x3 matrix. The product of a 2x2 matrix and a 2x3 matrix will result in a 2x3 matrix. Let's denote the elements of matrix H as h_ij, where i is the row index and j is the column index. We will calculate each element of H using the formula for matrix multiplication: h_ij = f_i1 * e_1j + f_i2 * e_2j.Calculate h_11: First, we calculate the element h_11 of matrix H. This is the element in the first row and first column of the resulting matrix. Using the formula for matrix multiplication, we have: h_11 = f_11 * e_11 + f_12 * e_21 h_11 = 1 * 0 + 2 * 3 h_11 = 0 + 6 h_11 = 6Calculate h_12: Next, we calculate the element h_12 of matrix H. This is the element in the first row and second column of the resulting matrix. Using the formula for matrix multiplication, we have: h_12 = f_11 * e_12 + f_12 * e_22 h_12 = 1 * (-1) + 2 * 2 h_12 = -1 + 4 h_12 = 3Calculate h_13: Now, we calculate the element h_13 of matrix H. This is the element in the first row and third column of the resulting matrix. Using the formula for matrix multiplication, we have: h_13 = f_11 * e_13 + f_12 * e_23 h_13 = 1 * 5 + 2 * 1 h_13 = 5 + 2 h_13 = 7Calculate h_21: We move on to calculate the element h_21 of matrix H. This is the element in the second row and first column of the resulting matrix. Using the formula for matrix multiplication, we have: h_21 = f_21 * e_11 + f_22 * e_21 h_21 = (-2) * 0 + 3 * 3 h_21 = 0 + 9 h_21 = 9Calculate h_22: Next, we calculate the element h_22 of matrix H. This is the element in the second row and second column of the resulting matrix. Using the formula for matrix multiplication, we have: h_22 = f_21 * e_12 + f_22 * e_22 h_22 = (-2) * (-1) + 3 * 2 h_22 = 2 + 6 h_22 = 8Calculate h_23: Finally, we calculate the element h_23 of matrix H. This is the element in the second row and third column of the resulting matrix. Using the formula for matrix multiplication, we have: h_23 = f_21 * e_13 + f_22 * e_23 h_23 = (-2) * 5 + 3 * 1 h_23 = -10 + 3 h_23 = -7Complete Matrix H: Now that we have calculated all the elements of matrix H, we can write down the complete matrix H as follows: H = [[h_11, h_12, h_13],      [h_21, h_22, h_23]] H = [[6, 3, 7],      [9, 8, -7]]

$\begin{array}{l} F=\left[\begin{array}{rr} 1 & 2 \\ -2 & 3 \end{array}\right] \text { and } E=\left[\begin{array}{rrr} 0 & -1 & 5 \\ 3 & 2 & 1 \end{array}\right] \end{array}$ $\newline$ Let $\mathrm{H}=\mathrm{FE}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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