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

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.Verify matrix multiplication possibility: Verify if matrix multiplication is possible. Matrix E has dimensions 2x3 (2 rows and 3 columns), and matrix B has dimensions 3x2 (3 rows and 2 columns). Since the number of columns in E is equal to the number of rows in B, matrix multiplication is possible.Set up the multiplication: Set up the multiplication. To find H, we need to multiply each row of E by each column of B and sum the products. The resulting matrix H will have dimensions 2x2.Calculate first element of matrix H: Calculate the first element of matrix H. Multiply the first row of E by the first column of B: H[1,1] = (1*1) + (4*2) + (2*2) = 1 + 8 + 4 = 13Calculate second element first row H: Calculate the second element of the first row of matrix H. Multiply the first row of E by the second column of B: H[1,2] = (1*3) + (4*3) + (2*(-2)) = 3 + 12 - 4 = 11Calculate first element second row H: Calculate the first element of the second row of matrix H. Multiply the second row of E by the first column of B: H[2,1] = (1*1) + (2*2) + (2*2) = 1 + 4 + 4 = 9Calculate second element second row H: Calculate the second element of the second row of matrix H. Multiply the second row of E by the second column of B: H[2,2] = (1*3) + (2*3) + (2*(-2)) = 3 + 6 - 4 = 5Combine results form matrix H: Combine the results to form matrix H. H = [[13, 11], [9, 5]]

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

H=[quad]

$E=\left[\begin{array}{lll}1 & 4 & 2 \\ 1 & 2 & 2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{rr}1 & 3 \\ 2 & 3 \\ 2 & -2\end{array}\right]$ $\newline$ 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

E=\left[\begin{array}{lll}1 & 4 & 2 \\ 1 & 2 & 2\end{array}\right]

and

\mathrm{B}=\left[\begin{array}{rr}1 & 3 \\ 2 & 3 \\ 2 & -2\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.
Verify matrix multiplication possibility: Verify if matrix multiplication is possible. $\newline$ Matrix $E$ has dimensions $2 \times 3$ ( $2$ rows and $3$ columns), and matrix $B$ has dimensions $3 \times 2$ ( $3$ rows and $2$ columns). Since the number of columns in $E$ is equal to the number of rows in $B$ , matrix multiplication is possible.
Set up the multiplication: Set up the multiplication. $\newline$ To find $H$ , we need to multiply each row of $E$ by each column of $B$ and sum the products. The resulting matrix $H$ will have dimensions $2 \times 2$ .
Calculate first element of matrix H: Calculate the first element of matrix H. Multiply the first row of $E$ by the first column of $B$ : $H[1,1] = (1 \times 1) + (4 \times 2) + (2 \times 2) = 1 + 8 + 4 = 13$
Calculate second element first row H: Calculate the second element of the first row of matrix $H$ . Multiply the first row of $E$ by the second column of $B$ : $H[1,2] = (1 \times 3) + (4 \times 3) + (2 \times (-2)) = 3 + 12 - 4 = 11$
Calculate first element second row $H$ : Calculate the first element of the second row of matrix $H$ . Multiply the second row of $E$ by the first column of $B$ : $H[2,1] = (1 \times 1) + (2 \times 2) + (2 \times 2) = 1 + 4 + 4 = 9$
Calculate second element second row $H$ : Calculate the second element of the second row of matrix $H$ . Multiply the second row of $E$ by the second column of $B$ : $H[2,2] = (1 \times 3) + (2 \times 3) + (2 \times (-2)) = 3 + 6 - 4 = 5$
Combine results form matrix $\newline$ $H$ : Combine the results to form matrix $\newline$ $H$ . $\newline$ $\newline$ H = \left[\begin{array}{cc}$\newline$$13$ & $11$ (\newline\)$9$ & $5$$\newline$\end{array}\right] $\newline$