E=[[5,5,1],[4,0,3]] and B=[[-1,5],[1,2],[-2,3]] Let H=EB. Find H. H=

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. E is a 2x3 matrix and B is a 3x2 matrix, so we can multiply E by B to get a 2x2 matrix H.Set up the multiplication: Set up the multiplication. We will calculate each element of matrix H by taking the dot product of the corresponding row from E and the corresponding column from B.Calculate first element of H: Calculate the first element of matrix H. H[1,1] = (5 * -1) + (5 * 1) + (1 * -2) = -5 + 5 - 2 = -2Calculate second element of first row: Calculate the second element of the first row of matrix H. H[1,2] = (5 * 5) + (5 * 2) + (1 * 3) = 25 + 10 + 3 = 38Calculate first element of second row: Calculate the first element of the second row of matrix H. H[2,1] = (4 * -1) + (0 * 1) + (3 * -2) = -4 + 0 - 6 = -10Calculate second element of second row: Calculate the second element of the second row of matrix H. H[2,2] = (4 * 5) + (0 * 2) + (3 * 3) = 20 + 0 + 9 = 29Combine results for matrix H: Combine the results to form matrix H. H = [[-2, 38], [-10, 29]]

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E=[[5,5,1],[4,0,3]] and
B=[[-1,5],[1,2],[-2,3]]
Let
H=EB. Find
H.

H=

$\mathrm{E}=\left[\begin{array}{lll}5 & 5 & 1 \\ 4 & 0 & 3\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{rr}-1 & 5 \\ 1 & 2 \\ -2 & 3\end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{EB}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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Math Problems

Algebra 1

Unions and intersections of sets

Full solution

\mathrm{E}=\left[\begin{array}{lll}5 & 5 & 1 \\ 4 & 0 & 3\end{array}\right]

and

\mathrm{B}=\left[\begin{array}{rr}-1 & 5 \\ 1 & 2 \\ -2 & 3\end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{EB}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand matrix multiplication: Understand matrix multiplication. $\newline$ 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. $\newline$ $E$ is a $2 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, so we can multiply $E$ by $B$ to get a $2 \times 2$ matrix $H$ .
Set up the multiplication: Set up the multiplication. $\newline$ We will calculate each element of matrix $H$ by taking the dot product of the corresponding row from $E$ and the corresponding column from $B$ .
Calculate first element of H: Calculate the first element of matrix $H$ . $H[1,1] = (5 \times -1) + (5 \times 1) + (1 \times -2) = -5 + 5 - 2 = -2$
Calculate second element of first row: Calculate the second element of the first row of matrix $H$ . $H[1,2] = (5 \times 5) + (5 \times 2) + (1 \times 3) = 25 + 10 + 3 = 38$
Calculate first element of second row: Calculate the first element of the second row of matrix $H$ . $H[2,1] = (4 \times -1) + (0 \times 1) + (3 \times -2) = -4 + 0 - 6 = -10$
Calculate second element of second row: Calculate the second element of the second row of matrix $H$ . $H[2,2] = (4 \times 5) + (0 \times 2) + (3 \times 3) = 20 + 0 + 9 = 29$
Combine results for matrix $H$ : Combine the results to form matrix $H$ .H = \begin{bmatrix}-2 & 38\-10 & 29\end{bmatrix}