D=[[1,0],[-1,5]] and B=[[1,0,2],[4,5,4]] Let H=DB. Find H. H=[quad]

Understand matrix multiplication: Understand matrix multiplication. Matrix multiplication involves taking the rows of the first matrix (D) and columns of the second matrix (B) and performing dot products to get the entries of the resulting matrix (H). The number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be defined. In this case, D is a 2x2 matrix and B is a 2x3 matrix, so the multiplication is defined and will result in a 2x3 matrix.Perform first row multiplication: Perform the multiplication for the first row of H. The first row of H will be obtained by multiplying the first row of D by each column of B. H[1,1] = (1 * 1) + (0 * 4) = 1 H[1,2] = (1 * 0) + (0 * 5) = 0 H[1,3] = (1 * 2) + (0 * 4) = 2 So the first row of H is [1, 0, 2].Perform second row multiplication: Perform the multiplication for the second row of H. The second row of H will be obtained by multiplying the second row of D by each column of B. H[2,1] = (-1 * 1) + (5 * 4) = -1 + 20 = 19 H[2,2] = (-1 * 0) + (5 * 5) = 0 + 25 = 25 H[2,3] = (-1 * 2) + (5 * 4) = -2 + 20 = 18 So the second row of H is [19, 25, 18].

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D=[[1,0],[-1,5]] and

B=[[1,0,2],[4,5,4]]
Let
H=DB. Find
H.

H=[quad]

$\mathrm{D}=\left[\begin{array}{rr}1 & 0 \\ -1 & 5\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{lll} 1 & 0 & 2 \\ 4 & 5 & 4 \end{array}\right]$ $\newline$ Let $\mathrm{H}=\mathrm{DB}$ . Find $\mathrm{H}$ . $\newline$ $\mathbf{H}=$

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Math Problems

Algebra 1

Unions and intersections of sets

Full solution

\mathrm{D}=\left[\begin{array}{rr}1 & 0 \\ -1 & 5\end{array}\right]

and

\mathrm{B}=\left[\begin{array}{lll} 1 & 0 & 2 \\ 4 & 5 & 4 \end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{DB}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand matrix multiplication: Understand matrix multiplication. Matrix multiplication involves taking the rows of the first matrix $D$ and columns of the second matrix $B$ and performing dot products to get the entries of the resulting matrix $H$ . The number of columns in the first matrix must equal the number of rows in the second matrix for the multiplication to be defined. In this case, $D$ is a $2 \times 2$ matrix and $B$ is a $2 \times 3$ matrix, so the multiplication is defined and will result in a $2 \times 3$ matrix.
Perform first row multiplication: Perform the multiplication for the first row of $H$ . The first row of $H$ will be obtained by multiplying the first row of $D$ by each column of $B$ . $H[1,1] = (1 \times 1) + (0 \times 4) = 1$ $H[1,2] = (1 \times 0) + (0 \times 5) = 0$ $H[1,3] = (1 \times 2) + (0 \times 4) = 2$ So the first row of $H$ is $[1, 0, 2]$ .
Perform second row multiplication: Perform the multiplication for the second row of $H$ . The second row of $H$ will be obtained by multiplying the second row of $D$ by each column of $B$ . $H[2,1] = (-1 \times 1) + (5 \times 4) = -1 + 20 = 19$ $H[2,2] = (-1 \times 0) + (5 \times 5) = 0 + 25 = 25$ $H[2,3] = (-1 \times 2) + (5 \times 4) = -2 + 20 = 18$ So the second row of $H$ is $[19, 25, 18]$ .