The value of A+B is \(\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)\) and the value of 3A is \(\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)\) .
How to add two matrices?
To add two matrices, we have to add the element present in the same position in the respective matrices.
(A+B)ij= Aij + Bij
where i is the no. of row and j is the no. of column.
How to multiply a scalar by the matrix?
In order to multiply a scalar by the matrix, we have to multiply that scalar with every element of the matrix.
nA= nAij
Here given matrix is
A= \(\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)\)
and the other matrix is
B= \(\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)\)
The sum of the matrix is A+B= \(\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)\)+ \(\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)\)
⇒ A+B =\(\left(\begin{array}{ccc}2+1&-3+0\\0+10&5+(-1/2)\\7+3&-2+1\end{array}\right)\)
⇒ A+B= \(\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)\)
the value of 3A= 3 \(\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)\)= \(\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)\)
Therefore the value of A+B is \(\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)\) and the value of 3A is \(\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)\) .
Learn more about the addition of matrices
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