How to find matrice A and B
Home
/
How to find matrice A and B
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Step-by-step explanation:
Hope this answer will help you
Thank you
Verified answer
[tex]\large\underline{\sf{Solution-}}[/tex]
Given matrices are
[tex]\rm :\longmapsto\:2A + B = \bigg[ \begin{matrix}3& - 4 \\ 2&7 \end{matrix} \bigg] - - - (1)[/tex]
and
[tex]\rm :\longmapsto\:A - 2B = \bigg[ \begin{matrix}4&3 \\ 1&1 \end{matrix} \bigg] - - - (2)[/tex]
Now,
Multiply equation (1) by 2, we get
[tex]\rm :\longmapsto\:4A + 2B = \bigg[ \begin{matrix}6& - 8 \\ 4&14 \end{matrix} \bigg] - - - (3)[/tex]
Now, Adding equation (2) and (3), we get
[tex]\rm :\longmapsto\:5A= \bigg[ \begin{matrix}6& - 8 \\ 4&14 \end{matrix} \bigg] + \bigg[ \begin{matrix}4&3 \\ 1&1 \end{matrix} \bigg][/tex]
[tex]\rm :\longmapsto\:5A= \bigg[ \begin{matrix}6 + 4& - 8 + 3 \\ 4 + 1&14 + 1 \end{matrix} \bigg] [/tex]
[tex]\rm :\longmapsto\:5A= \bigg[ \begin{matrix}10& - 5 \\ 5&15 \end{matrix} \bigg] [/tex]
[tex]\bf :\longmapsto\:A= \bigg[ \begin{matrix}2& -1 \\ 1&3 \end{matrix} \bigg] [/tex]
On substituting the value of A, in equation (1), we get
[tex]\rm :\longmapsto\:2\bigg[ \begin{matrix}2& -1 \\ 1&3 \end{matrix} \bigg] + B = \bigg[ \begin{matrix}3& - 4 \\ 2&7 \end{matrix} \bigg] [/tex]
[tex]\rm :\longmapsto\:\bigg[ \begin{matrix}4& -2 \\ 2&6 \end{matrix} \bigg] + B = \bigg[ \begin{matrix}3& - 4 \\ 2&7 \end{matrix} \bigg] [/tex]
[tex]\rm :\longmapsto\: B = \bigg[ \begin{matrix}3& - 4 \\ 2&7 \end{matrix} \bigg] - \bigg[ \begin{matrix}4& -2 \\ 2&6 \end{matrix} \bigg][/tex]
[tex]\rm :\longmapsto\: B = \bigg[ \begin{matrix}3 - 4& - 4 + 2 \\ 2 - 2&7 - 6 \end{matrix} \bigg][/tex]
[tex]\bf :\longmapsto\: B = \bigg[ \begin{matrix} - 1& -2 \\ 0&1 \end{matrix} \bigg][/tex]
Hence,
[tex] \red{\bf :\longmapsto\:A= \bigg[ \begin{matrix}2& -1 \\ 1&3 \end{matrix} \bigg]}[/tex]
and
[tex] \red{\bf :\longmapsto\: B = \bigg[ \begin{matrix} - 1& -2 \\ 0&1 \end{matrix} \bigg]}[/tex]
Additional Information :-
1. Matrix addition of two matrices A and B is possible only when order of both the matrices A and B are same.
2. Matrix subtraction of two matrices A and B is possible only when order of both the matrices A and B are same.
3. Matrix multiplication is defined when number of columns of pre - multiplier is equal to number of rows of post - multiplier.