F=[[5],[0],[4]]" and "A=[[-1,1]] Let H=FA. Find H. H=[]

Understand matrix multiplication: Understand matrix multiplication. Matrix multiplication involves taking the rows of the first matrix (F) and multiplying them by the columns of the second matrix (A), then summing the products to get the entries of the resulting matrix (H).Identify matrix dimensions: Identify the dimensions of the matrices. Matrix F is a 3x1 matrix and matrix A is a 1x2 matrix. The resulting matrix H will have the dimensions of the outer dimensions, which is 3x2.Multiply first row of F: Multiply the first row of F by the only column of A. The first row of F is [5], and the only column of A is [-1, 1]. Multiplying these, we get: 5 * -1 = -5 5 * 1 = 5 So the first row of H will be [-5, 5].Multiply second row of F: Multiply the second row of F by the only column of A. The second row of F is [0], and the only column of A is [-1, 1]. Multiplying these, we get: 0 * -1 = 0 0 * 1 = 0 So the second row of H will be [0, 0].Multiply third row of F: Multiply the third row of F by the only column of A. The third row of F is [4], and the only column of A is [-1, 1]. Multiplying these, we get: 4 * -1 = -4 4 * 1 = 4 So the third row of H will be [-4, 4].Combine results for matrix H: Combine the results to form the matrix H. Combining the results from steps 3, 4, and 5, we get the matrix H: H = [[-5, 5], [0, 0], [-4, 4]]

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F=[[5],[0],[4]]" and "A=[[-1,1]]
Let
H=FA. Find
H.

H=[]

$\mathrm{F}=\left[\begin{array}{l} 5 \\ 0 \\ 4 \end{array}\right] \text { and } \mathrm{A}=\left[\begin{array}{ll} -1 & 1 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{FA}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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Algebra 1

Unions and intersections of sets

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\mathrm{F}=\left[\begin{array}{l} 5 \\ 0 \\ 4 \end{array}\right] \text { and } \mathrm{A}=\left[\begin{array}{ll} -1 & 1 \end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{FA}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand matrix multiplication: Understand matrix multiplication. Matrix multiplication involves taking the rows of the first matrix $F$ and multiplying them by the columns of the second matrix $A$ , then summing the products to get the entries of the resulting matrix $H$ .
Identify matrix dimensions: Identify the dimensions of the matrices. $\newline$ Matrix $F$ is a $3 \times 1$ matrix and matrix $A$ is a $1 \times 2$ matrix. The resulting matrix $H$ will have the dimensions of the outer dimensions, which is $3 \times 2$ .
Multiply first row of F: Multiply the first row of $F$ by the only column of $A$ . The first row of $F$ is $[5]$ , and the only column of $A$ is $[-1, 1]$ . Multiplying these, we get: $5 \times -1 = -5$ $5 \times 1 = 5$ So the first row of $H$ will be $[-5, 5]$ .
Multiply second row of F: Multiply the second row of F by the only column of A. $\newline$ The second row of F is $[0]$ , and the only column of A is $[-1, 1]$ . Multiplying these, we get: $\newline$ $0 \times -1 = 0$ $\newline$ $0 \times 1 = 0$ $\newline$ So the second row of H will be $[0, 0]$ .
Multiply third row of F: Multiply the third row of $F$ by the only column of $A$ . The third row of $F$ is $[4]$ , and the only column of $A$ is $[-1, 1]$ . Multiplying these, we get: $4 \times -1 = -4$ $4 \times 1 = 4$ So the third row of $H$ will be $[-4, 4]$ .
Combine results for matrix $H$ : Combine the results to form the matrix $H$ . Combining the results from steps $3$ , $4$ , and $5$ , we get the matrix $H$ : $H = \left[\begin{array}{cc} -5 & 5 \ 0 & 0 \ -4 & 4 \end{array}\right]$