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melomori [17]
3 years ago
6

10. Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain wh

y.

Mathematics
1 answer:
Artemon [7]3 years ago
5 0

Answer(a):

Order of matrix A = 3x3 {because number of rows=3, number of columns=3}

Order of matrix B = 3x3

Order of matrix C = 1x3


3A will be of order 3x3 because multiply by scalar doesn't change the order. Which is same as the order of matrix B.

So 3A+B is possible.

We simply multiply all elements of A with 3 and add them with corresponding elements of B.

3\begin{bmatrix}2 &  -1& 0\\ 0 &  5& 0.3\\ 1 &  4&10 \end{bmatrix}+\begin{bmatrix}5 &  0& 2\\ 1 &  -3& 9\\ 2 &  0& 4\end{bmatrix}= \begin{bmatrix}11 &  -3& 2\\ 1 &  12& 9.9\\ 5 &  12& 34\end{bmatrix}


Answer(b):

2B will be of order 3x3 because multiply by scalar doesn't change the order. Which is NOT same as the order of matrix C.

So 2B+C is NOT possible.

Answer(c):

CA is possible only if

number of columns of C = number of columns of A

3=3

which is true hence CA is possible.

\begin{bmatrix}1 &3  &5 \end{bmatrix}*\begin{bmatrix}2 &  -1& 0\\ 0 &  5& 0.3\\ 1 &  4&10 \end{bmatrix}=\begin{bmatrix}1*2+3*0+5*1 & 1*-1+3*5+5*4 & 1*0+3*0.3+5*10\end{bmatrix}

= \begin{bmatrix}7 &  34& 50.9\end{bmatrix}

<em><u>If the matrix is not visible properly then look at the attached picture.</u></em>

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