A=[[-1],[4],[4]]" and "F=[[0,-2]] Let H=AF. Find H. H=[]

Define Matrices A and F: Define the matrices A and F. Matrix A is given as A = [[-1], [4], [4]] which is a 3x1 matrix. Matrix F is given as F = [[0, -2]] which is a 1x2 matrix. To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, A has 1 column and F has 1 row, so the multiplication is possible.Perform Matrix Multiplication: Perform the matrix multiplication H = AF. To multiply A by F, we take each element of A and multiply it by each element of F, then sum the products to get the elements of the resulting matrix H. H = [[-1 * 0 + (-1) * (-2)], [4 * 0 + 4 * (-2)], [4 * 0 + 4 * (-2)]] This simplifies to: H = [[2], [-8], [-8]]Verify Resulting Matrix Dimensions: Verify the dimensions of the resulting matrix H. After the multiplication, we should have a matrix with the same number of rows as A and the same number of columns as F. Since A is 3x1 and F is 1x2, the resulting matrix H should be 3x2.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A=[[-1],[4],[4]]" and "F=[[0,-2]]
Let
H=AF. Find
H.

H=[]

$A=\left[\begin{array}{r} -1 \\ 4 \\ 4 \end{array}\right] \text { and } \mathrm{F}=\left[\begin{array}{ll} 0 & -2 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{AF}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

View step-by-step help

Home

Math Problems

Algebra 1

Unions and intersections of sets

Full solution

A=\left[\begin{array}{r} -1 \\ 4 \\ 4 \end{array}\right] \text { and } \mathrm{F}=\left[\begin{array}{ll} 0 & -2 \end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{AF}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Define Matrices $A$ and $F$ : Define the matrices $A$ and $F$ . $\newline$ Matrix $A$ is given as $A = [[-1], [4], [4]]$ which is a $3 \times 1$ matrix. $\newline$ Matrix $F$ is given as $F = [[0, -2]]$ which is a $1 \times 2$ matrix. $\newline$ To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, $A$ has $F$ $1$ column and $F$ has $F$ $1$ row, so the multiplication is possible.
Perform Matrix Multiplication: Perform the matrix multiplication $H = AF$ . To multiply $A$ by $F$ , we take each element of $A$ and multiply it by each element of $F$ , then sum the products to get the elements of the resulting matrix $H$ . $H = [[-1 \times 0 + (-1) \times (-2)], [4 \times 0 + 4 \times (-2)], [4 \times 0 + 4 \times (-2)]]$ This simplifies to: $H = [[2], [-8], [-8]]$
Verify Resulting Matrix Dimensions: Verify the dimensions of the resulting matrix $H$ . After the multiplication, we should have a matrix with the same number of rows as $A$ and the same number of columns as $F$ . Since $A$ is $3 \times 1$ and $F$ is $1 \times 2$ , the resulting matrix $H$ should be $3 \times 2$ .