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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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Compare linear, exponential, and quadratic growth

Full solution

Q.

\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]\)

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