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D=[[2,3],[1,1],[5,-2]]" and "F=[[2,5],[2,2]]
Let
H=DF. Find
H.

H=[]

$\mathrm{D}=\left[\begin{array}{rr} 2 & 3 \\ 1 & 1 \\ 5 & -2 \end{array}\right] \text { and } \mathrm{F}=\left[\begin{array}{ll} 2 & 5 \\ 2 & 2 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{DF}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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Compare linear, exponential, and quadratic growth

Full solution

Q.

\mathrm{D}=\left[\begin{array}{rr} 2 & 3 \\ 1 & 1 \\ 5 & -2 \end{array}\right] \text { and } \mathrm{F}=\left[\begin{array}{ll} 2 & 5 \\ 2 & 2 \end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{DF}

. Find

\mathrm{H}

.

\newline

\mathbf{H}=

Define Matrices D and F: Define the matrices D and F. Matrix D is a $3 \times 2$ matrix given by $D=\left[\begin{array}{cc}2 & 3 \ 1 & 1 \ 5 & -2\end{array}\right]$ . Matrix F is a $2 \times 2$ matrix given by $F=\left[\begin{array}{cc}2 & 5 \ 2 & 2\end{array}\right]$ . To find the product $H$ of $D$ and $F$ , we need to perform matrix multiplication.
Verify Matrix Multiplication: Verify if matrix multiplication is possible. Matrix multiplication is possible if the number of columns in the first matrix is equal to the number of rows in the second matrix. Matrix $D$ has $2$ columns and matrix $F$ has $2$ rows, so multiplication is possible.
Perform Matrix Multiplication: Perform the matrix multiplication. $\newline$ To multiply $D$ by $F$ , we take the dot product of the rows of $D$ with the columns of $F$ . The resulting matrix $H$ will have the same number of rows as $D$ and the same number of columns as $F$ , so $H$ will be a $3 \times 2$ matrix. $\newline$ For $H[1,1]$ , we calculate $F$ $0$ . $\newline$ For $F$ $1$ , we calculate $F$ $2$ . $\newline$ For $F$ $3$ , we calculate $F$ $4$ . $\newline$ For $F$ $5$ , we calculate $F$ $6$ . $\newline$ For $F$ $7$ , we calculate $F$ $8$ . $\newline$ For $F$ $9$ , we calculate $D$ $0$ . $\newline$ So the matrix $H$ is: $\newline$ $D$ $2$

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