E=[[1,-1,1],[2,3,4]] and A=[[2,4],[2,-2],[-1,5]] Let H=EA. Find H. H=[◻]◻

Question

E=[[1,-1,1],[2,3,4]] and  A=[[2,4],[2,-2],[-1,5]] Let  H=EA. Find  H.  H=[◻]◻

Bytelearn · Accepted Answer

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. 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 dimensions: Verify the dimensions of matrices E and A. Matrix E has dimensions 2x3 (2 rows and 3 columns), and matrix A has dimensions 3x2 (3 rows and 2 columns). Since the number of columns in E is equal to the number of rows in A, we can multiply these matrices.Set up multiplication: Set up the multiplication of matrices E and A. To multiply E by A, we will calculate the sum of the products of the corresponding entries from the rows of E and the columns of A.Calculate first entry of H: Calculate the first entry of matrix H. For the entry in the first row and first column of H, we multiply the corresponding elements of the first row of E with the first column of A and sum them up: H[1,1] = (1*2) + (-1*2) + (1*-1) = 2 - 2 - 1 = -1Calculate second entry of H: Calculate the second entry of the first row of matrix H. For the entry in the first row and second column of H, we multiply the corresponding elements of the first row of E with the second column of A and sum them up: H[1,2] = (1*4) + (-1*-2) + (1*5) = 4 + 2 + 5 = 11Calculate first entry of second row: Calculate the first entry of the second row of matrix H. For the entry in the second row and first column of H, we multiply the corresponding elements of the second row of E with the first column of A and sum them up: H[2,1] = (2*2) + (3*2) + (4*-1) = 4 + 6 - 4 = 6Calculate second entry of second row: Calculate the second entry of the second row of matrix H. For the entry in the second row and second column of H, we multiply the corresponding elements of the second row of E with the second column of A and sum them up: H[2,2] = (2*4) + (3*-2) + (4*5) = 8 - 6 + 20 = 22Combine results for matrix H: Combine the results to form matrix H. We combine the results from steps 4 to 7 to form the resulting matrix H: H = [[-1, 11], [6, 22]]

$\mathrm{E}=\left[\begin{array}{rrr}1 & -1 & 1 \\ 2 & 3 & 4\end{array}\right]$ and $A=\left[\begin{array}{rr}2 & 4 \\ 2 & -2 \\ -1 & 5\end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{EA}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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