B=[[4,4],[1,0],[-2,1]]" and "F=[[0,3],[0,1]] Let H=BF. Find H. H=[]

Question

B=[[4,4],[1,0],[-2,1]]" and "F=[[0,3],[0,1]] Let  H=BF. Find  H.  H=[]

Bytelearn · Accepted Answer

Understand matrix multiplication rules: Understand matrix multiplication rules. To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Matrix B is a 3x2 matrix and matrix F is a 2x2 matrix, so they can be multiplied.Set up the multiplication: Set up the multiplication. We will calculate the entries of matrix H by taking the dot product of the rows of B with the columns of F.Calculate first entry of H: Calculate the first entry of matrix H. The first entry of H is the dot product of the first row of B with the first column of F. H[1,1] = (4 * 0) + (4 * 0) = 0Calculate second entry of H: Calculate the second entry of matrix H. The second entry of H is the dot product of the first row of B with the second column of F. H[1,2] = (4 * 3) + (4 * 1) = 12 + 4 = 16Calculate third entry of H: Calculate the third entry of matrix H. The third entry of H is the dot product of the second row of B with the first column of F. H[2,1] = (1 * 0) + (0 * 0) = 0Calculate fourth entry of H: Calculate the fourth entry of matrix H. The fourth entry of H is the dot product of the second row of B with the second column of F. H[2,2] = (1 * 3) + (0 * 1) = 3 + 0 = 3Calculate fifth entry of H: Calculate the fifth entry of matrix H. The fifth entry of H is the dot product of the third row of B with the first column of F. H[3,1] = (-2 * 0) + (1 * 0) = 0Calculate sixth entry of H: Calculate the sixth entry of matrix H. The sixth entry of H is the dot product of the third row of B with the second column of F. H[3,2] = (-2 * 3) + (1 * 1) = -6 + 1 = -5

$B=\left[\begin{array}{rr} 4 & 4 \\ 1 & 0 \\ -2 & 1 \end{array}\right] \text { and } F=\left[\begin{array}{ll} 0 & 3 \\ 0 & 1 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{BF}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

Full solution

More problems from Write and solve direct variation equations

Related topics