Use the given matrices to evaluate the expression.$A=\begin{bmatrix}4&1\\-3&0\end{bmatrix}$A=[4 1−3 0] , $B=\begin{bmatrix}5&-2\\6&-1\end{bmatrix}$B=[5 −26 −1] , $C=\begin{bmatrix}1&0\\0&1\end{bmatrix}$C=[1 00 1]$\frac{1}{2}$12 $\left(AB\right)=$(AB)=
Question
Use the given matrices to evaluate the expression.A=[4 1−3 0] , B=[5 −26 −1] , C=[1 00 1]12 (AB)=
Solution
To evaluate the expression, we first need to multiply matrices A and B.
Matrix multiplication is done element by element with corresponding elements in the row of the first matrix and the column of the second matrix.
So,
AB = [ (45 + 16) (4*-2 + 1*-1) (-35 + 06) (-3*-2 + 0*-1) ]
AB = [ (20 + 6) (-8 -1) (-15 + 0) (6 + 0) ]
AB = [ 26 -9 -15 6 ]
Now, we multiply this result by 1/2:
1/2 * AB = 1/2 * [ 26 -9 -15 6 ]
= [ 13 -4.5 -7.5 3 ]
So, 1/2(AB) = [ 13 -4.5 -7.5 3 ]
Similar Questions
Use the given matrices to evaluate the expression.$A=\begin{bmatrix}4&1\\-3&0\end{bmatrix}$A=[4 1−3 0] , $B=\begin{bmatrix}5&-2\\6&-1\end{bmatrix}$B=[5 −26 −1] , $C=\begin{bmatrix}1&0\\0&1\end{bmatrix}$C=[1 00 1]$\frac{1}{2}$12 $\left(AB\right)=$(AB)=
Consider the matrices and .Calculate .
Use the given matrices to evaluate the expression.$A=\begin{bmatrix}9&-6\\7&5\end{bmatrix},\ B=\begin{bmatrix}4&3\\-7&-6\end{bmatrix},\ C=\begin{bmatrix}0.5&3.6\\2.4&-3.2\end{bmatrix}$A=[9 −67 5], B=[4 3−7 −6], C=[0.5 3.62.4 −3.2]$A+B+10C=$A+B+10C=
(4 marks)Let A = (aij ) be the 4 × 4 matrix and D = (dij ) be the 4 × 1 matrix shown below.A =−3 1 1 01 1 2 −20 1 1 21 1 2 1 D =−1101(a) Evaluate4∑j=1a4j a2j
matrix A=[1 0,2 4, -1 2], d is a scalar which is d=2. calculate A-d
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.