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If $\left[ \begin{matrix} 2a+3b & a-b \\ \end{matrix} \right]=\left[ \begin{matrix} 19 & 2 \\ \end{matrix} \right]$. Find the values of a and b.
If $\left[ \begin{matrix} 2a+3b & a-b \\ \end{matrix} \right]=\left[ \begin{matrix} 19 & 2 \\ \end{matrix} \right]$. Find the values of a and b.
Class 10 | Frank | ICSE | Maths | Matrices
If $\left[ \begin{matrix} 2a+3b & a-b \\ \end{matrix} \right]=\left[ \begin{matrix} 19 & 2 \\ \end{matrix} \right]$. Find the values of a and b.

According to given question,

$2a+3b=19$ … (i)

$a–b=2$ … (ii)

$a=2+b$

Now, substituting the value of a in equation (i) we get,

$2(2+b)+3b=19$

$4+2b+3b=19$

$5b=19–4$

$5b=15$

$b=15/5$

$b=3$

So, $a=2+b$

$=2+3$

$=5$

Hence, the value of a is $5$ and b is $3$.

i

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