D=[[-1,0,4],[2,0,0]] and F=[[-1,1],[-1,3],[2,4]] Let H=DF. Find H. H=[]

Understand matrix multiplication: Understand matrix multiplication. Matrix multiplication involves taking the rows of the first matrix (D) and columns of the second matrix (F) and performing dot products to get the entries of the new matrix (H). The number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be defined. In this case, matrix D is a 2x3 matrix and matrix F is a 3x2 matrix, so their product will be a 2x2 matrix.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 D and the first column of F: H[1,1] = D[1,1]*F[1,1] + D[1,2]*F[2,1] + D[1,3]*F[3,1] H[1,1] = (-1)*(-1) + (0)*(-1) + (4)*(2) H[1,1] = 1 + 0 + 8 H[1,1] = 9Calculate 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 D and the second column of F: H[1,2] = D[1,1]*F[1,2] + D[1,2]*F[2,2] + D[1,3]*F[3,2] H[1,2] = (-1)*(1) + (0)*(3) + (4)*(4) H[1,2] = -1 + 0 + 16 H[1,2] = 15Calculate 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 D and the first column of F: H[2,1] = D[2,1]*F[1,1] + D[2,2]*F[2,1] + D[2,3]*F[3,1] H[2,1] = (2)*(-1) + (0)*(-1) + (0)*(2) H[2,1] = -2 + 0 + 0 H[2,1] = -2Calculate 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 D and the second column of F: H[2,2] = D[2,1]*F[1,2] + D[2,2]*F[2,2] + D[2,3]*F[3,2] H[2,2] = (2)*(1) + (0)*(3) + (0)*(4) H[2,2] = 2 + 0 + 0 H[2,2] = 2Combine results to form H: Combine the results to form matrix H. We have calculated all four entries of the matrix H, so we can now form the matrix: H = [[9, 15], [-2, 2]]

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D=[[-1,0,4],[2,0,0]] and
F=[[-1,1],[-1,3],[2,4]]
Let
H=DF. Find
H.

H=[]

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

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Math Problems

Algebra 1

Unions and intersections of sets

Full solution

\mathrm{D}=\left[\begin{array}{rrr}-1 & 0 & 4 \\ 2 & 0 & 0\end{array}\right]

and

F=\left[\begin{array}{rr}-1 & 1 \\ -1 & 3 \\ 2 & 4\end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{DF}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand matrix multiplication: Understand matrix multiplication. Matrix multiplication involves taking the rows of the first matrix $D$ and columns of the second matrix $F$ and performing dot products to get the entries of the new matrix $H$ . The number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be defined. In this case, matrix $D$ is a $2 \times 3$ matrix and matrix $F$ is a $3 \times 2$ matrix, so their product will be a $2 \times 2$ matrix.
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 $D$ and the first column of $F$ : $H[1,1] = D[1,1]\cdot F[1,1] + D[1,2]\cdot F[2,1] + D[1,3]\cdot F[3,1]$ $H[1,1] = (-1)\cdot(-1) + (0)\cdot(-1) + (4)\cdot(2)$ $H[1,1] = 1 + 0 + 8$ $H[1,1] = 9$
Calculate second entry of H: Calculate the second entry of matrix H. $\newline$ The second entry of H is the dot product of the first row of D and the second column of F: $\newline$ $H[1,2] = D[1,1]\cdot F[1,2] + D[1,2]\cdot F[2,2] + D[1,3]\cdot F[3,2]$ $\newline$ $H[1,2] = (-1)\cdot(1) + (0)\cdot(3) + (4)\cdot(4)$ $\newline$ $H[1,2] = -1 + 0 + 16$ $\newline$ $H[1,2] = 15$
Calculate third entry of H: Calculate the third entry of matrix H. $\newline$ The third entry of H is the dot product of the second row of D and the first column of F: $\newline$ $H[2,1] = D[2,1]\cdot F[1,1] + D[2,2]\cdot F[2,1] + D[2,3]\cdot F[3,1]$ $\newline$ $H[2,1] = (2)\cdot(-1) + (0)\cdot(-1) + (0)\cdot(2)$ $\newline$ $H[2,1] = -2 + 0 + 0$ $\newline$ $H[2,1] = -2$
Calculate fourth entry of H: Calculate the fourth entry of matrix H. $\newline$ The fourth entry of H is the dot product of the second row of D and the second column of F: $\newline$ $H[2,2] = D[2,1]\cdot F[1,2] + D[2,2]\cdot F[2,2] + D[2,3]\cdot F[3,2]$ $\newline$ $H[2,2] = (2)\cdot(1) + (0)\cdot(3) + (0)\cdot(4)$ $\newline$ $H[2,2] = 2 + 0 + 0$ $\newline$ $H[2,2] = 2$
Combine results to form $H$ : Combine the results to form matrix $H$ . We have calculated all four entries of the matrix $H$ , so we can now form the matrix: $H = \left[\begin{array}{cc} 9 & 15 \ -2 & 2 \end{array}\right]$