F=[[0,4],[5,2]]" and "D=[[2,5],[3,0]] Let H=FD. Find H. H=[]

Understand matrix multiplication: Understand matrix multiplication. To multiply two matrices, we take the dot product of the rows of the first matrix with the columns of the second matrix. The number of columns in the first matrix must be equal to the number of rows in the second matrix for multiplication to be possible.Set up matrix multiplication: Set up the multiplication of matrix F by matrix D. Matrix F is a 2x2 matrix and matrix D is also a 2x2 matrix, so their multiplication is possible and will result in another 2x2 matrix H.Calculate first element of H: Calculate the first element of matrix H. The first element of matrix H (H[1,1]) is the dot product of the first row of F and the first column of D. H[1,1] = F[1,1]*D[1,1] + F[1,2]*D[2,1] = 0*2 + 4*3 = 0 + 12 = 12Calculate second element of H: Calculate the second element of matrix H. The second element of matrix H (H[1,2]) is the dot product of the first row of F and the second column of D. H[1,2] = F[1,1]*D[1,2] + F[1,2]*D[2,2] = 0*5 + 4*0 = 0 + 0 = 0Calculate third element of H: Calculate the third element of matrix H. The third element of matrix H (H[2,1]) is the dot product of the second row of F and the first column of D. H[2,1] = F[2,1]*D[1,1] + F[2,2]*D[2,1] = 5*2 + 2*3 = 10 + 6 = 16Calculate fourth element of H: Calculate the fourth element of matrix H. The fourth element of matrix H (H[2,2]) is the dot product of the second row of F and the second column of D. H[2,2] = F[2,1]*D[1,2] + F[2,2]*D[2,2] = 5*5 + 2*0 = 25 + 0 = 25

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

F=[[0,4],[5,2]]" and "D=[[2,5],[3,0]]
Let
H=FD. Find
H.

H=[]

$\mathrm{F}=\left[\begin{array}{ll} 0 & 4 \\ 5 & 2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 2 & 5 \\ 3 & 0 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{FD}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

View step-by-step help

Home

Math Problems

Algebra 1

Unions and intersections of sets

Full solution

\mathrm{F}=\left[\begin{array}{ll} 0 & 4 \\ 5 & 2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 2 & 5 \\ 3 & 0 \end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{FD}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand matrix multiplication: Understand matrix multiplication. To multiply two matrices, we take the dot product of the rows of the first matrix with the columns of the second matrix. The number of columns in the first matrix must be equal to the number of rows in the second matrix for multiplication to be possible.
Set up matrix multiplication: Set up the multiplication of matrix $F$ by matrix $D$ . Matrix $F$ is a $2 \times 2$ matrix and matrix $D$ is also a $2 \times 2$ matrix, so their multiplication is possible and will result in another $2 \times 2$ matrix $H$ .
Calculate first element of H: Calculate the first element of matrix $H$ . The first element of matrix $H$ ( $H[1,1]$ ) is the dot product of the first row of $F$ and the first column of $D$ . $H[1,1] = F[1,1]\times D[1,1] + F[1,2]\times D[2,1] = 0\times 2 + 4\times 3 = 0 + 12 = 12$
Calculate second element of H: Calculate the second element of matrix H. The second element of matrix H $H[1,2]$ is the dot product of the first row of F and the second column of D. $H[1,2] = F[1,1]\times D[1,2] + F[1,2]\times D[2,2] = 0\times 5 + 4\times 0 = 0 + 0 = 0$
Calculate third element of H: Calculate the third element of matrix $H$ . The third element of matrix $H$ ( $H[2,1]$ ) is the dot product of the second row of $F$ and the first column of $D$ . $H[2,1] = F[2,1]\cdot D[1,1] + F[2,2]\cdot D[2,1] = 5\cdot 2 + 2\cdot 3 = 10 + 6 = 16$
Calculate fourth element of H: Calculate the fourth element of matrix H. $\newline$ The fourth element of matrix H $H[2,2]$ is the dot product of the second row of F and the second column of D. $\newline$ $H[2,2] = F[2,1]\cdot D[1,2] + F[2,2]\cdot D[2,2] = 5\cdot 5 + 2\cdot 0 = 25 + 0 = 25$