E=[[-1,4],[5,2]] and C=[[1,2],[-1,1]]. Let H=EC. Find H. H=[quad]

Understand matrix multiplication: Understand matrix multiplication. To multiply two matrices, we take the dot product of the rows of the first matrix with the columns of the second matrix. The number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be defined.Set up matrix multiplication: Set up the multiplication of matrices E and C. E = [[-1, 4], [5, 2]] C = [[1, 2], [-1, 1]] We will calculate the entries of the resulting matrix H by multiplying the rows of E by the columns of C.Calculate H[1,1]: Calculate the entry H[1,1]. This is the dot product of the first row of E with the first column of C. H[1,1] = (-1 * 1) + (4 * -1) = -1 - 4 = -5Calculate H[1,2]: Calculate the entry H[1,2]. This is the dot product of the first row of E with the second column of C. H[1,2] = (-1 * 2) + (4 * 1) = -2 + 4 = 2Calculate H[2,1]: Calculate the entry H[2,1]. This is the dot product of the second row of E with the first column of C. H[2,1] = (5 * 1) + (2 * -1) = 5 - 2 = 3Calculate H[2,2]: Calculate the entry H[2,2]. This is the dot product of the second row of E with the second column of C. H[2,2] = (5 * 2) + (2 * 1) = 10 + 2 = 12Combine results for matrix H: Combine the results to form the matrix H. H = [[-5, 2], [3, 12]]

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E=[[-1,4],[5,2]] and
C=[[1,2],[-1,1]].
Let
H=EC. Find
H.

H=[quad]

$\mathrm{E}=\left[\begin{array}{rr}-1 & 4 \\ 5 & 2\end{array}\right]$ and $C=\left[\begin{array}{rr}1 & 2 \\ -1 & 1\end{array}\right]$ . $\newline$ Let $\mathrm{H}=\mathrm{EC}$ . 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}{rr}-1 & 4 \\ 5 & 2\end{array}\right]

and

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

\newline

Let

\mathrm{H}=\mathrm{EC}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand matrix multiplication: Understand matrix multiplication. To multiply two matrices, we take the dot product of the rows of the first matrix with the columns of the second matrix. The number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be defined.
Set up matrix multiplication: Set up the multiplication of matrices $E$ and $C$ . $E = \left[\begin{array}{cc}-1 & 4 \ 5 & 2\end{array}\right]$ $C = \left[\begin{array}{cc}1 & 2 \ -1 & 1\end{array}\right]$ We will calculate the entries of the resulting matrix $H$ by multiplying the rows of $E$ by the columns of $C$ .
Calculate $H[1,1]$ : Calculate the entry $H[1,1]$ . This is the dot product of the first row of $E$ with the first column of $C$ . $H[1,1] = (-1 \times 1) + (4 \times -1) = -1 - 4 = -5$
Calculate $H[1,2]$ : Calculate the entry $H[1,2]$ . This is the dot product of the first row of $E$ with the second column of $C$ . $H[1,2] = (-1 \times 2) + (4 \times 1) = -2 + 4 = 2$
Calculate $H[2,1]$ : Calculate the entry $H[2,1]$ . This is the dot product of the second row of $E$ with the first column of $C$ . $H[2,1] = (5 \times 1) + (2 \times -1) = 5 - 2 = 3$
Calculate $H[2,2]$ : Calculate the entry $H[2,2]$ . This is the dot product of the second row of $E$ with the second column of $C$ . $H[2,2] = (5 \times 2) + (2 \times 1) = 10 + 2 = 12$
Combine results for matrix $H$ : Combine the results to form the matrix $H$ . $H = \begin{bmatrix}-5 & 2 \ 3 & 12\end{bmatrix}$