Chapter 12.1, Problem 27PPE

To determine

To simplify: the given matrix expression.

Answer to Problem 27PPE

  $\left[\begin{array}{l}-12.6-21.92.1\\ 8.1-27.935.4\\ 10.824.6-14.4\end{array}\right]-\left[\begin{array}{l}-15.68.2-1.4\\ 160-1.6\\ 2.8-11.8-6.6\end{array}\right]=\left[\begin{array}{l}3.6-30.13.5\\ -7.9-27.937.0\\ 8.036.4-7.8\end{array}\right]$ .

Explanation of Solution

Given:

The given matrix is $-3\left[\begin{array}{l}4.2-7.30.7\\ 2.7-9.311.8\\ 3.68.2-4.8\end{array}\right]-2\left[\begin{array}{l}7.8-4.10.7\\ -800.8\\ -1.45.93.3\end{array}\right]$ .

Concept used:

Scalar multiplication of the matrix: scalar multiplication refers to the product of a real number and a matrix. In scalar multiplication, each element in the matrix is multiplied by the given scalar. 

The sum or differences of the any matrix is possible, when the number of elements of both matrices are same. i.e. number of columns are same and number of rows are same.

Calculation:

The given matrix is $-3\left[\begin{array}{l}4.2-7.30.7\\ 2.7-9.311.8\\ 3.68.2-4.8\end{array}\right]-2\left[\begin{array}{l}7.8-4.10.7\\ -800.8\\ -1.45.93.3\end{array}\right]$ .

Here number of elements in both matrices are same.

Therefore, first apply the scaler multiplication and then subtract the matrix. Now,

Now, subtract the elements pf the given matrices. Then,

Hence, the simplified form of the given matrix is

  $\left[\begin{array}{l}-12.6-21.92.1\\ 8.1-27.935.4\\ 10.824.6-14.4\end{array}\right]-\left[\begin{array}{l}-15.68.2-1.4\\ 160-1.6\\ 2.8-11.8-6.6\end{array}\right]=\left[\begin{array}{l}3.6-30.13.5\\ -7.9-27.937.0\\ 8.036.4-7.8\end{array}\right]$ .