Chapter 14, Problem 25P

(a)

To determine

Perform the mathematical operation of $\left[A\right]+\left[B\right]$ for the given matrices using Excel.

Answer to Problem 25P

The mathematical operation $\left[A\right]+\left[B\right]$ for the given matrices is performed by using excel.

Explanation of Solution

Given data:

$\left[A\right]=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$, $\left[B\right]=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$, $\left[C\right]=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$.

Calculation:

To find $\left[A\right]+\left[B\right]$:

Refer to the Figure 1:

First type the appropriate characters and values in the Excel sheet. In the cell A6, type the operation as “$\left[A\right]+\left[B\right]=$”. Next in the cell B5, type as “=B1:D3+F1:H3”. Here, B1:D3 is done by select using left mouse button, pick cells B1 through D3 and F1:H3 is done by select by using left mouse button, pick cells F1 through H3. Then holding down the ctrl and the Shift Key, press the Enter key. The result obtained for the cell B5 as 5.

Likewise select by using left mouse button, pick cells from B5 through D7 and click in the formula bar, then holding down the ctrl and the Shift Key, press the Enter key. Thus, the result is obtained as shown in Figure 2.

Conclusion:

Hence, the mathematical operation $\left[A\right]+\left[B\right]$ for the given matrices has been performed using Excel.

(b)

To determine

Perform the mathematical operation of $\left[A\right]-\left[B\right]$ for the given matrices using Excel.

Answer to Problem 25P

The mathematical operation $\left[A\right]-\left[B\right]$ for the given matrices is performed by using excel.

Explanation of Solution

Given data:

$\left[A\right]=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$, $\left[B\right]=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$, $\left[C\right]=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$.

Calculation:

To find $\left[A\right]-\left[B\right]$:

Refer to the Figure 3:

First type the appropriate characters and values in the Excel sheet. In the cell A7, type the operation as “$\left[A\right]-\left[B\right]=$”. Next in the cell B6, type as “=B1:D3-F1:H3”. Here, B1:D3 is done by select using left mouse button, pick cells B1 through D3 and F1:H3 is done by select by using left mouse button, pick cells F1 through H3. Then holding down the ctrl and the Shift Key, press the Enter key. The result obtained for the cell B5 as 3.

Likewise select by using left mouse button, pick cells from B6 through D8 and click in the formula bar, then holding down the ctrl and the Shift Key, press the Enter key. Thus, the result is obtained as shown in Figure 4.

Conclusion:

Hence, the mathematical operation $\left[A\right]-\left[B\right]$ for the given matrices has been performed using Excel.

(c)

To determine

Perform the mathematical operation $3\left[A\right]$ for the given matrices using Excel.

Answer to Problem 25P

The mathematical operation $3\left[A\right]$ for the given matrices is performed by using excel.

Explanation of Solution

Given data:

$\left[A\right]=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$, $\left[B\right]=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$, $\left[C\right]=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$.

Calculation:

To find $3\left[A\right]$:

Refer to the Figure 5:

First type the appropriate characters and values in the Excel sheet. In the cell A6, type the operation as “$3\left[A\right]=$”. Next in the cell B5, type as “=3*(B1:D3)”. Here, B1:D3 is done by select using left mouse button, pick cells B1 through D3. Then holding down the ctrl and the Shift Key, press the Enter key. The result obtained for the cell B5 as 12.

Likewise select by using left mouse button, pick cells from B5 through D7 and click in the formula bar, then holding down the ctrl and the Shift Key, press the Enter key. Thus, the result is obtained as shown in Figure 6.

Conclusion:

Hence, the mathematical operation $3\left[A\right]$ for the given matrices has been performed using Excel.

(d)

To determine

Perform the mathematical operation of $\left[A\right]\left[B\right]$ for the given matrices using Excel.

Answer to Problem 25P

The mathematical operation $\left[A\right]\left[B\right]$ for the given matrices is performed by using excel.

Explanation of Solution

Given data:

$\left[A\right]=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$, $\left[B\right]=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$, $\left[C\right]=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$.

Calculation:

To find $\left[A\right]\left[B\right]$:

Refer to the Figure 7:

First type the appropriate characters and values in the Excel sheet. In the cell A6, type the operation as “$\left[A\right]\left[B\right]=$”. Next in the cell B5, type as “=MMULT(B1:D3,F1:H3)”. Here, B1:D3 is done by select using left mouse button, pick cells B1 through D3 and F1:H3 is done by select by using left mouse button, pick cells F1 through H3. Then holding down the ctrl and the Shift Key, press the Enter key. The result obtained for the cell B5 as 18.

Likewise select by using left mouse button, pick cells from B5 through D7 and click in the formula bar, then holding down the ctrl and the Shift Key, press the Enter key. Thus, the result is obtained as shown in Figure 8.

Conclusion:

Hence, the mathematical operation $\left[A\right]\left[B\right]$ for the given matrices has been performed using Excel.

(e)

To determine

Perform the mathematical operation of $\left[A\right]\left\{C\right\}$ for the given matrices using Excel.

Answer to Problem 25P

The mathematical operation $\left[A\right]\left\{C\right\}$ for the given matrices is performed by using excel.

Explanation of Solution

Given data:

$\left[A\right]=\left[\begin{array}{ccc}4& 2& 1\\ 7& 0& -7\\ 1& -5& 3\end{array}\right]$, $\left[B\right]=\left[\begin{array}{ccc}1& 2& -1\\ 5& 3& 3\\ 4& 5& -7\end{array}\right]$, $\left[C\right]=\left[\begin{array}{c}1\\ -2\\ 4\end{array}\right]$.

Calculation:

To find $\left[A\right]\left\{C\right\}$:

Refer to the Figure 9:

First type the appropriate characters and values in the Excel sheet. In the cell A6, type the operation as “$\left[A\right]\left\{C\right\}=$”. Next in the cell B5, type as “=MMULT(B1:D3,J1:J3)”. Here, B1:D3 is done by select using left mouse button, pick cells B1 through D3 and J1:J3 is done by select by using left mouse button, pick cells J1 through J3. Then holding down the ctrl and the Shift Key, press the Enter key. The result obtained for the cell B5 as 4.

Likewise select by using left mouse button, pick cells from B5 through B7 and click in the formula bar, then holding down the ctrl and the Shift Key, press the Enter key. Thus, the result is obtained as shown in Figure 10.

Conclusion:

Hence, the mathematical operation $\left[A\right]\left\{C\right\}$ for the given matrices has been performed using Excel.