Chapter 4, Problem 2STP

To determine

Tofind:the product of two matrices if possible.

Answer to Problem 2STP

There is no option given so it’s not possible for this given matrix.

Explanation of Solution

Given:

  $\left[\begin{array}{cc}3& 1\end{array}\right].\left[\begin{array}{c}2\\ 5\end{array}\right]$

Concept used:

Example:

  $a_{11}$ here the sum of the position $1+1=2$ is even so multiply the value by $\left(1\right)$ .

  $a_{12}$ here the sum of the position $1+2=3$ is odd so multiply the value by $\left(-1\right)$ .

Mathematically:

  $\left|\text{A}\right|\text{=}\left|{\text{a}}_{\text{11}}{\text{.minor of a}}_{\text{11}}\text{+}\left(\text{-1}\right){\text{a}}_{\text{12}}{\text{.minor of a}}_{\text{12}}{\text{+a}}_{\text{13}}{\text{.minor of a}}_{13}\right|$ .

Calculation:

Here $\left[\begin{array}{cc}3& 1\end{array}\right].\left[\begin{array}{c}2\\ 5\end{array}\right]$ .

Using matrix multiplication:

  $\left[\begin{array}{cc}3& 1\end{array}\right].\left[\begin{array}{c}2\\ 5\end{array}\right]=\left[3\times 2+5\times 1\right]=\left[11\right]$ .

Hence there is no option given so it’s not possible for this given matrix.

Hence determinant of matrix $\text{A}$ = $\text{34}$ .