Let A=left[begin{array}{ll}2 & 4 3 & 2end{array}right], B=left[begin{array}{cc}1 & 3 -2

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3 and 4 .Determinants and Matrices

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Let $A=\left[\begin{array}{ll}2 & 4 \\ 3 & 2\end{array}\right], B=\left[\begin{array}{cc}1 & 3 \\ -2 & 5\end{array}\right], C=\left[\begin{array}{cc}-2 & 5 \\ 3 & 4\end{array}\right]$

Find $AB$

A

$\left[ {\begin{array}{*{20}{l}}
{ - 6}&{26} \\
{ - 1}&{19}
\end{array}} \right]$

B

$\left[ {\begin{array}{*{20}{l}}
{ - 6}&{26} \\
{ - 1}&{19}
\end{array}} \right]$

C

$\left[ {\begin{array}{*{20}{l}}
{ - 6}&{26} \\
{ - 1}&{19}
\end{array}} \right]$

D

$\left[ {\begin{array}{*{20}{l}}
{ - 6}&{26} \\
{ - 1}&{19}
\end{array}} \right]$

Solution

Matrix $A$ has $2$ columns. This number is equal to the number of rows in matrix $B$. Therefore, $AB $ is defined as :

$AB = \left[ {\begin{array}{*{20}{l}}
2&4 \\
3&2
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1&3 \\
{ – 2}&5
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{l}}
{2(1) + 4( – 2)}&{2(3) + 4(5)} \\
{3(1) + 2( – 2)}&{3(3) + 2(5)}
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{l}}
{2 – 8}&{6 + 20} \\
{3 – 4}&{9 + 10}
\end{array}} \right]$

$ = \left[ {\begin{array}{*{20}{l}}
{ – 6}&{26} \\
{ – 1}&{19}
\end{array}} \right]$

Standard 12

Mathematics

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