Chapter 12.1, Problem 1P

a.

To determine

To find: the sum or differences of the given matrix.

Answer to Problem 1P

  $\left[\begin{array}{l}5\\ 3.2\\ -4.9\end{array}\right]+\left[\begin{array}{l}-9\\ -1.7\\ -11.1\end{array}\right]=\left[\begin{array}{l}-4\\ 1.5\\ -17.0\end{array}\right]$ .

Explanation of Solution

Given:

The given matrix is $\left[\begin{array}{l}5\\ 3.2\\ -4.9\end{array}\right]+\left[\begin{array}{l}-9\\ -1.7\\ -11.1\end{array}\right]$ .

Concept used:

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 $\left[\begin{array}{l}5\\ 3.2\\ -4.9\end{array}\right]+\left[\begin{array}{l}-9\\ -1.7\\ -11.1\end{array}\right]$ .

Here number of elements in both matrices are same.

Therefore, add the matrix. Now,

  $\left[\begin{array}{l}5\\ 3.2\\ -4.9\end{array}\right]+\left[\begin{array}{l}-9\\ -1.7\\ -11.1\end{array}\right]=\left[\begin{array}{l}5+\left(-9\right)\\ 3.2+\left(-1.7\right)\\ -4.9+\left(-11.1\right)\end{array}\right]=\left[\begin{array}{l}-4\\ 1.5\\ -17.0\end{array}\right]$

Hence, the sum of the given matrix is $\left[\begin{array}{l}5\\ 3.2\\ -4.9\end{array}\right]+\left[\begin{array}{l}-9\\ -1.7\\ -11.1\end{array}\right]=\left[\begin{array}{l}-4\\ 1.5\\ -17.0\end{array}\right]$ .

b.

To determine

To find: the sum or differences of the given matrix.

Answer to Problem 1P

  $\left[\begin{array}{l}-40\\ 37\end{array}\right]-\left[\begin{array}{l}-5-1\\ 0.5-3\end{array}\right]=\left[\begin{array}{l}11\\ 2.54\end{array}\right]$ .

Explanation of Solution

Given:

The given matrix is $\left[\begin{array}{l}-40\\ 37\end{array}\right]-\left[\begin{array}{l}-5-1\\ 0.5-3\end{array}\right]$ .

Concept used:

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 $\left[\begin{array}{l}-40\\ 37\end{array}\right]-\left[\begin{array}{l}-5-1\\ 0.5-3\end{array}\right]$ .

Here number of elements in both matrices are same.

Therefore, subtract the matrix. Now,

  $\begin{array}{l}\left[\begin{array}{l}-40\\ 37\end{array}\right]-\left[\begin{array}{l}-5-1\\ 0.5-3\end{array}\right]=\left[\begin{array}{l}-4-\left(-5\right)0-\left(-1\right)\\ 3-0.57-\left(-3\right)\end{array}\right]\\ =\left[\begin{array}{l}-4+50+1\\ 2.57-3\end{array}\right]\\ =\left[\begin{array}{l}11\\ 2.54\end{array}\right]\end{array}$

Hence, the sum of the given matrix is $\left[\begin{array}{l}-40\\ 37\end{array}\right]-\left[\begin{array}{l}-5-1\\ 0.5-3\end{array}\right]=\left[\begin{array}{l}11\\ 2.54\end{array}\right]$ .

c.

To determine

To explain: that the sum or differences of the matrix cannot be added when they are not the same size.

Explanation of Solution

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

Therefore, when they are not same, the addition and subtraction is not possible.