B=[[1,4],[1,3]]" and "D=[[4,3],[0,-1]] Let H=BD. Find H. H=[]

Define Matrices B and D: Define the matrices B and D. Matrix B is given as B=[[1,4],[1,3]] and matrix D is given as D=[[4,3],[0,-1]]. We need to multiply these matrices to find H.Recall Matrix Multiplication Rule: Recall the matrix multiplication rule. To multiply two matrices, we sum the products of the rows of the first matrix with the corresponding columns of the second matrix.Calculate First Element of Matrix H: Calculate the first element of matrix H. The first element of H (H[1,1]) is the sum of the products of the first row of B and the first column of D. H[1,1] = (1*4) + (4*0) = 4 + 0 = 4Calculate Second Element of First Row: Calculate the second element of the first row of matrix H. The second element of the first row of H (H[1,2]) is the sum of the products of the first row of B and the second column of D. H[1,2] = (1*3) + (4*-1) = 3 - 4 = -1Calculate First Element of Second Row: Calculate the first element of the second row of matrix H. The first element of the second row of H (H[2,1]) is the sum of the products of the second row of B and the first column of D. H[2,1] = (1*4) + (3*0) = 4 + 0 = 4Calculate Second Element of Second Row: Calculate the second element of the second row of matrix H. The second element of the second row of H (H[2,2]) is the sum of the products of the second row of B and the second column of D. H[2,2] = (1*3) + (3*-1) = 3 - 3 = 0Combine Calculated Elements: Combine the calculated elements to form matrix H. H = [[H[1,1], H[1,2]], [H[2,1], H[2,2]]] H = [[4, -1], [4, 0]]

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B=[[1,4],[1,3]]" and "D=[[4,3],[0,-1]]
Let
H=BD. Find
H.

H=[]

$\mathrm{B}=\left[\begin{array}{ll} 1 & 4 \\ 1 & 3 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{rr} 4 & 3 \\ 0 & -1 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{BD}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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Math Problems

Algebra 1

Unions and intersections of sets

Full solution

\mathrm{B}=\left[\begin{array}{ll} 1 & 4 \\ 1 & 3 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{rr} 4 & 3 \\ 0 & -1 \end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{BD}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Define Matrices B and D: Define the matrices B and D. Matrix B is given as B=\left[\begin{array}{cc}1 & 4\1 & 3\end{array}\right] and matrix D is given as D=\left[\begin{array}{cc}4 & 3\0 & -1\end{array}\right]. We need to multiply these matrices to find $H$ .
Recall Matrix Multiplication Rule: Recall the matrix multiplication rule. $\newline$ To multiply two matrices, we sum the products of the rows of the first matrix with the corresponding columns of the second matrix.
Calculate First Element of Matrix H: Calculate the first element of matrix H. The first element of H $H[1,1]$ is the sum of the products of the first row of B and the first column of D. $H[1,1] = (1 \times 4) + (4 \times 0) = 4 + 0 = 4$
Calculate Second Element of First Row: Calculate the second element of the first row of matrix $H$ . The second element of the first row of $H$ ( $H[1,2]$ ) is the sum of the products of the first row of $B$ and the second column of $D$ . $H[1,2] = (1 \times 3) + (4 \times -1) = 3 - 4 = -1$
Calculate First Element of Second Row: Calculate the first element of the second row of matrix $H$ . The first element of the second row of $H$ ( $H[2,1]$ ) is the sum of the products of the second row of $B$ and the first column of $D$ . $H[2,1] = (1 \times 4) + (3 \times 0) = 4 + 0 = 4$
Calculate Second Element of Second Row: Calculate the second element of the second row of matrix $H$ . The second element of the second row of $H$ ( $H[2,2]$ ) is the sum of the products of the second row of $B$ and the second column of $D$ . $H[2,2] = (1 \times 3) + (3 \times -1) = 3 - 3 = 0$
Combine Calculated Elements: Combine the calculated elements to form matrix $H$ . $H = \left[\begin{array}{cc}H[1,1] & H[1,2]\ H[2,1] & H[2,2]\end{array}\right]$ $H = \left[\begin{array}{cc}4 & -1\ 4 & 0\end{array}\right]$