{:[D=[[2,0],[4,1]]" and "],[C=[[2,4,4],[4,2,4]]]:} Let H=DC. Find H. H=[]

Define Matrices D and C: Define the matrices D and C. Matrix D is a 2x2 matrix given by: D = [[2, 0], [4, 1]] Matrix C is a 2x3 matrix given by: C = [[2, 4, 4], [4, 2, 4]] To find the product H = DC, we need to multiply matrix D by matrix C.Verify Matrix Multiplication: Verify if the matrix multiplication is possible. Matrix multiplication is possible if the number of columns in the first matrix (D) is equal to the number of rows in the second matrix (C). Matrix D has 2 columns and matrix C has 2 rows, so the multiplication is possible.Perform Matrix Multiplication: Perform the matrix multiplication. To multiply the matrices, we take the dot product of the rows of the first matrix with the columns of the second matrix. H[1,1] = (2 * 2) + (0 * 4) = 4 + 0 = 4 H[1,2] = (2 * 4) + (0 * 2) = 8 + 0 = 8 H[1,3] = (2 * 4) + (0 * 4) = 8 + 0 = 8 H[2,1] = (4 * 2) + (1 * 4) = 8 + 4 = 12 H[2,2] = (4 * 4) + (1 * 2) = 16 + 2 = 18 H[2,3] = (4 * 4) + (1 * 4) = 16 + 4 = 20 So the product matrix H is: H = [[4, 8, 8], [12, 18, 20]]

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{:[D=[[2,0],[4,1]]" and "],[C=[[2,4,4],[4,2,4]]]:}
Let
H=DC. Find
H.

H=[]

$\begin{array}{l} \mathrm{D}=\left[\begin{array}{ll} 2 & 0 \\ 4 & 1 \end{array}\right] \text { and } \mathrm{C}=\left[\begin{array}{lll} 2 & 4 & 4 \\ 4 & 2 & 4 \end{array}\right] \end{array}$ $\newline$ Let $\mathrm{H}=\mathrm{DC}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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Algebra 1

Compare linear, exponential, and quadratic growth

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\begin{array}{l} \mathrm{D}=\left[\begin{array}{ll} 2 & 0 \\ 4 & 1 \end{array}\right] \text { and } \mathrm{C}=\left[\begin{array}{lll} 2 & 4 & 4 \\ 4 & 2 & 4 \end{array}\right] \end{array}

\newline

Let

\mathrm{H}=\mathrm{DC}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Define Matrices D and C: Define the matrices D and C. $\newline$ Matrix D is a $2$ x $2$ matrix given by: $\newline$ D = \left[\begin{array}{cc}$\newline2 & 0 (\newline$4 & 1 $\newline$ \end{array}\right]\) $\newline$ Matrix C is a $2$ x $3$ matrix given by: $\newline$ C = \left[\begin{array}{ccc}$\newline2 & 4 & 4 (\newline$4 & 2 & 4 $\newline$ \end{array}\right]\) $\newline$ To find the product $H = DC$ , we need to multiply matrix D by matrix C.
Verify Matrix Multiplication: Verify if the matrix multiplication is possible. Matrix multiplication is possible if the number of columns in the first matrix $D$ is equal to the number of rows in the second matrix $C$ . Matrix $D$ has $2$ columns and matrix $C$ has $2$ rows, so the multiplication is possible.
Perform Matrix Multiplication: Perform the matrix multiplication. $\newline$ To multiply the matrices, we take the dot product of the rows of the first matrix with the columns of the second matrix. $\newline$ $H[1,1] = (2 \times 2) + (0 \times 4) = 4 + 0 = 4$ $\newline$ $H[1,2] = (2 \times 4) + (0 \times 2) = 8 + 0 = 8$ $\newline$ $H[1,3] = (2 \times 4) + (0 \times 4) = 8 + 0 = 8$ $\newline$ $H[2,1] = (4 \times 2) + (1 \times 4) = 8 + 4 = 12$ $\newline$ $H[2,2] = (4 \times 4) + (1 \times 2) = 16 + 2 = 18$ $\newline$ $H[2,3] = (4 \times 4) + (1 \times 4) = 16 + 4 = 20$ $\newline$ So the product matrix $H$ is: $\newline$ H = \left[\begin{array}{ccc}$\newline4 & 8 & 8, (\newline$12 & 18 & 20 $\newline$ \end{array}\right]\)