B=[[0],[-1],[2]] and A=[[1,2]] Let H=BA. Find H. H=[]

Understand Matrix Dimensions: First, let's understand the dimensions of the matrices B and A. Matrix B is a 3x1 matrix and matrix A 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, B has 1 column and A has 1 row, so we can multiply B by A.Perform Matrix Multiplication: Next, we perform the matrix multiplication BA. The resulting matrix H will have the same number of rows as B and the same number of columns as A, which means H will be a 3x2 matrix. We calculate the entries of H by taking the dot product of the rows of B with the columns of A.Calculate Entries of Resulting Matrix: The calculation for each entry of H is as follows: H[1,1] = B[1,1] * A[1,1] = 0 * 1 = 0 H[1,2] = B[1,1] * A[1,2] = 0 * 2 = 0 H[2,1] = B[2,1] * A[1,1] = -1 * 1 = -1 H[2,2] = B[2,1] * A[1,2] = -1 * 2 = -2 H[3,1] = B[3,1] * A[1,1] = 2 * 1 = 2 H[3,2] = B[3,1] * A[1,2] = 2 * 2 = 4Write Down Resulting Matrix: Now we can write down the resulting matrix H with the calculated entries: H = [[0, 0], [-1, -2], [2, 4]]

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

B=[[0],[-1],[2]] and
A=[[1,2]]
Let
H=BA. Find
H.

H=[]

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

View step-by-step help

Home

Math Problems

Algebra 1

Unions and intersections of sets

Full solution

\mathrm{B}=\left[\begin{array}{r}0 \\ -1 \\ 2\end{array}\right]

and

\mathrm{A}=\left[\begin{array}{ll}1 & 2\end{array}\right]

\newline

Let

\mathrm{H}=\mathrm{BA}

. Find

\mathrm{H}

\newline

\mathbf{H}=

Understand Matrix Dimensions: First, let's understand the dimensions of the matrices $B$ and $A$ . Matrix $B$ is a $3 \times 1$ matrix and matrix $A$ is a $1 \times 2$ 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, $B$ has $1$ column and $A$ has $1$ row, so we can multiply $B$ by $A$ .
Perform Matrix Multiplication: Next, we perform the matrix multiplication $BA$ . The resulting matrix $H$ will have the same number of rows as $B$ and the same number of columns as $A$ , which means $H$ will be a $3 \times 2$ matrix. We calculate the entries of $H$ by taking the dot product of the rows of $B$ with the columns of $A$ .
Calculate Entries of Resulting Matrix: The calculation for each entry of $H$ is as follows: $\newline$ $H[1,1] = B[1,1] \times A[1,1] = 0 \times 1 = 0$ $\newline$ $H[1,2] = B[1,1] \times A[1,2] = 0 \times 2 = 0$ $\newline$ $H[2,1] = B[2,1] \times A[1,1] = -1 \times 1 = -1$ $\newline$ $H[2,2] = B[2,1] \times A[1,2] = -1 \times 2 = -2$ $\newline$ $H[3,1] = B[3,1] \times A[1,1] = 2 \times 1 = 2$ $\newline$ $H[3,2] = B[3,1] \times A[1,2] = 2 \times 2 = 4$
Write Down Resulting Matrix: Now we can write down the resulting matrix $H$ with the calculated entries: $H = \begin{bmatrix} 0 & 0 \ -1 & -2 \ 2 & 4 \end{bmatrix}$