E=[[1,-1,5],[5,5,0]] and F=[[-2,-1],[5,2],[5,-2]] Let H=EF. Find H. H=

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 E is a 2x3 matrix and matrix F is a 3x2 matrix, so they can be multiplied to result in a 2x2 matrix H.Set up matrix multiplication: Set up the multiplication of matrices E and F. We will calculate the elements of matrix H by taking the dot product of the rows of E with the columns of F.Calculate H[1,1]: Calculate the element H[1,1]. H[1,1] = (1 * -2) + (-1 * 5) + (5 * 5) H[1,1] = -2 - 5 + 25 H[1,1] = 18Calculate H[1,2]: Calculate the element H[1,2]. H[1,2] = (1 * -1) + (-1 * 2) + (5 * -2) H[1,2] = -1 - 2 - 10 H[1,2] = -13Calculate H[2,1]: Calculate the element H[2,1]. H[2,1] = (5 * -2) + (5 * 5) + (0 * 5) H[2,1] = -10 + 25 + 0 H[2,1] = 15Calculate H[2,2): Calculate the element H[2,2]. H[2,2] = (5 * -1) + (5 * 2) + (0 * -2) H[2,2] = -5 + 10 + 0 H[2,2] = 5

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E=[[1,-1,5],[5,5,0]] and
F=[[-2,-1],[5,2],[5,-2]] Let
H=EF. Find
H.

H=

$\mathrm{E}=\left[\begin{array}{rrr}1 & -1 & 5 \\ 5 & 5 & 0\end{array}\right]$ and $F=\left[\begin{array}{rr}-2 & -1 \\ 5 & 2 \\ 5 & -2\end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{EF}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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Algebra 1

Write and solve direct variation equations

Full solution

\mathrm{E}=\left[\begin{array}{rrr}1 & -1 & 5 \\ 5 & 5 & 0\end{array}\right]

and

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

\newline

Let

\mathrm{H}=\mathrm{EF}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand matrix multiplication rules: Understand matrix multiplication rules. $\newline$ To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Matrix $E$ is a $2 \times 3$ matrix and matrix $F$ is a $3 \times 2$ matrix, so they can be multiplied to result in a $2 \times 2$ matrix $H$ .
Set up matrix multiplication: Set up the multiplication of matrices $E$ and $F$ . We will calculate the elements of matrix $H$ by taking the dot product of the rows of $E$ with the columns of $F$ .
Calculate $H[1,1]$ : Calculate the element $H[1,1]$ .
$H[1,1] = (1 \times -2) + (-1 \times 5) + (5 \times 5)$
$H[1,1] = -2 - 5 + 25$
$H[1,1] = 18$
Calculate $H[1,2]$ : Calculate the element $H[1,2]$ . $H[1,2] = (1 \times -1) + (-1 \times 2) + (5 \times -2)$ $H[1,2] = -1 - 2 - 10$ $H[1,2] = -13$
Calculate $H[2,1]$ : Calculate the element $H[2,1]$ .
$H[2,1] = (5 \times -2) + (5 \times 5) + (0 \times 5)$
$H[2,1] = -10 + 25 + 0$
$H[2,1] = 15$
Calculate $H[2,2)$ : Calculate the element $H[2,2]$ . $H[2,2] = (5 \times -1) + (5 \times 2) + (0 \times -2)$ $H[2,2] = -5 + 10 + 0$ $H[2,2] = 5$