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

Question

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

Bytelearn · Accepted Answer

Define Matrices D and F: Define the matrices D and F. Matrix D is a 3x2 matrix, and matrix F is a 2x2 matrix. D = [[-1, 0], [2, -2], [1, 3]] F = [[0, 2], [3, -2]]Verify Multiplication Possibility: Verify if the multiplication of D and F is possible. The number of columns in the first matrix (D) must be equal to the number of rows in the second matrix (F) to multiply them. D has 2 columns, and F has 2 rows, so multiplication is possible.Set Up Matrix Multiplication: Set up the multiplication of matrices D and F. To multiply the matrices, we take the dot product of the rows of D with the columns of F. This will result in a new matrix H which will have the same number of rows as D and the same number of columns as F.Calculate First Element of H: Calculate the first element of matrix H. Multiply the first row of D by the first column of F. H[1,1] = (-1 * 0) + (0 * 3) = 0Calculate Second Element of First Row: Calculate the second element of the first row of matrix H. Multiply the first row of D by the second column of F. H[1,2] = (-1 * 2) + (0 * -2) = -2Calculate First Element of Second Row: Calculate the first element of the second row of matrix H. Multiply the second row of D by the first column of F. H[2,1] = (2 * 0) + (-2 * 3) = -6Calculate Second Element of Second Row: Calculate the second element of the second row of matrix H. Multiply the second row of D by the second column of F. H[2,2] = (2 * 2) + (-2 * -2) = 4 + 4 = 8Calculate First Element of Third Row: Calculate the first element of the third row of matrix H. Multiply the third row of D by the first column of F. H[3,1] = (1 * 0) + (3 * 3) = 9Calculate Second Element of Third Row: Calculate the second element of the third row of matrix H. Multiply the third row of D by the second column of F. H[3,2] = (1 * 2) + (3 * -2) = 2 - 6 = -4Combine Elements to Form H: Combine the elements to form the matrix H. H = [[0, -2], [-6, 8], [9, -4]]

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

Full solution

More problems from Write and solve direct variation equations

Related topics