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Check whether it is possible to perform the indicated operation.$\begin{bmatrix}3&0\\1&5\end{bmatrix}\begin{bmatrix}2&-4\end{bmatrix}$[3 01 5][2 −4]​ResponsesPossiblePossibleNot possibleNot possibleQuestion 2If possible, find the product. If it is not possible, leave the box empty.$\begin{bmatrix}3&0\\1&5\end{bmatrix}\begin{bmatrix}2&-4\end{bmatrix}=$[3 01 5][2 −4]=​

Question

Check whether it is possible to perform the indicated operation.[3015][2−4]\begin{bmatrix}3&0\\1&5\end{bmatrix}\begin{bmatrix}2&-4\end{bmatrix}[3 01 5][2 −4]​ResponsesPossiblePossibleNot possibleNot possibleQuestion 2If possible, find the product. If it is not possible, leave the box empty.[3015][2−4]=\begin{bmatrix}3&0\\1&5\end{bmatrix}\begin{bmatrix}2&-4\end{bmatrix}=[3 01 5][2 −4]=​

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Solution

The operation is possible. The rule for matrix multiplication is that the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, the first matrix is a 2x2 matrix and the second matrix is a 1x2 matrix. Therefore, the operation can be performed.

To find the product, we multiply each element of the first row of the first matrix by the corresponding element of the second matrix and add the results. Then we do the same for the second row.

So, the product is:

[3015][2−4]=\begin{bmatrix}3&0\\1&5\end{bmatrix}\begin{bmatrix}2&-4\end{bmatrix}=

[(3∗2+0∗−4)(3∗−4+0∗2)(1∗2+5∗−4)(1∗−4+5∗2)]=\begin{bmatrix}(3*2+0*-4)&(3*-4+0*2)\\(1*2+5*-4)&(1*-4+5*2)\end{bmatrix}=

[6−12−186]\begin{bmatrix}6&-12\\-18&6\end{bmatrix}

This problem has been solved

Similar Questions

Check whether it is possible to perform the indicated operation.$\begin{bmatrix}3&0\\1&5\end{bmatrix}\begin{bmatrix}2&-4\end{bmatrix}$[3 01 5][2 −4]​ResponsesPossiblePossibleNot possibleNot possibleQuestion 2If possible, find the product. If it is not possible, leave the box empty.$\begin{bmatrix}3&0\\1&5\end{bmatrix}\begin{bmatrix}2&-4\end{bmatrix}=$[3 01 5][2 −4]=​

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Consider the matrices and  .Calculate .

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