Question

if a=[1 -2 3 -4 2 5] and b=[2 3 4 5 2 1] and ba=[bij],find b21+b32?

Answer 1

GIVEN :

The matrices are

$a=\left[\begin{array}{ccc} 1&-2&3\\ -4&2&5\end{array}\right]$

$b=\left[\begin{array}{cc} 2&5\\ 3&2\\ 4&1\end{array}\right]$

TO FIND :

The value of $b_{21}+b_{32}$

SOLUTION :

From the given matrices a and b  

$a=\left[\begin{array}{ccc} 1&-2&3\\ -4&2&5\end{array}\right]$

$b=\left[\begin{array}{cc} 2&5\\ 3&2\\ 4&1\end{array}\right]$

First find the matrix $ba=[b_{ij}]$

ba=$\left[\begin{array}{ccc} b_{11} & b_{12} & b_{13} \\ b_{21}& b_{22} &b_{23}\\ b_{31} & b_{32} & b_{33}\end{array}\right]$

Substitute the values in ba we get

ba=$\left[\begin{array}{ccc} 2-20 & -4+10 & 6+25\\ 3-8& -6+4 &9+10\\ 4-4& -8+2 &12+5\end{array}\right]$

ba=$\left[\begin{array}{ccc}-18&6&31\\ -5&-2&19\\ 0&-6&17\end{array}\right]$

Comparing the  above matrix with $ba=[b_{ij}]$ we get the values of $b_{21}=-5$ and $b_{32}=-6$

Now $b_{21}+b_{32}=-5-6$

By adding the like terms we get

$=-11$

$b_{21}+b_{32}=-11$

∴ the value of $b_{21}+b_{32}$ is -11

Answer 2

Answer:

-18

Step-by-step explanation

BA= $\left[\begin{array}{ccc}2&3\\4&5\\2&1\end{array}\right]$ $\left[\begin{array}{ccc}1&-2&3\\-4&2&5\\\end{array}\right]$ =$\left[\begin{array}{ccc}-10&2&21\\-16&2&37\\-2&-2&11\end{array}\right]$

Therefore;

$b_{21} +b_{32} =-16+-2\\\\b_{21} +b_{32}= -18$