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]$(AB)C=$(AB)C=
Question
Use the given matrices to evaluate the expression.A=[4 1−3 0] , B=[5 −26 −1] , C=[1 00 1](AB)C=
Solution
Sure, let's evaluate the expression step by step.
Step 1: Multiply matrices A and B.
The product of two matrices is calculated by multiplying the elements of each row of the first matrix with the elements of each column of the second matrix and adding the results.
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 ]
Step 2: Multiply the result (AB) with matrix C.
(AB)C = [ (261 + -90) (260 + -91) ] [ (-151 + 60) (-150 + 61) ]
(AB)C = [ (26 + 0) (0 - 9) ] [ (-15 + 0) (0 + 6) ]
(AB)C = [ 26 -9 ] [ -15 6 ]
So, the result of the expression (AB)C is the matrix [ 26 -9; -15 6 ].
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