Question

Find a and b if a{ 2 3] + b[-1 1] = [10 5]

Answer 1

${\boxed {a=3,b=-4}}$

${\large{\text{\underline{\underline{\red{Given :}}}}}}$

$a \left[\begin{array}{c}2\\3\end{array}\right] + b\left[\begin{array}{c}-1\\1 \end{array}\right] = \left[\begin{array}{c}10\\5\end{array}\right]$

${\large{\text{\underline{\underline{\red{To Find :}}}}}}$

$a \:\:\text{ and} \:\: b$

${\large{\text{\underline{\underline{\red{Solution :}}}}}}$

$a \left[\begin{array}{c}2\\3\end{array}\right] + b\left[\begin{array}{c}-1\\1 \end{array}\right] = \left[\begin{array}{c}10\\5\end{array}\right]$

$\left[\begin{array}{c}a(2)\\a(3)\end{array}\right] + \left[\begin{array}{c}b(-1)\\b(1 )\end{array}\right] = \left[\begin{array}{c}10\\5\end{array}\right]$

$\left[\begin{array}{c}2a\\3a\end{array}\right] + \left[\begin{array}{c}-b\\b \end{array}\right] = \left[\begin{array}{c}10\\5\end{array}\right]$

$\left[\begin{array}{c}2a+(-b)\\3a+b\end{array}\right] = \left[\begin{array}{c}10\\5\end{array}\right]$

$\left[\begin{array}{c}2a-b\\3a+b\end{array}\right] = \left[\begin{array}{c}10\\5\end{array}\right]$

$2a-b=10$_ _ _ _ _ $(1)$

$3a+b = 5$ _ _ _ _ _ $(2)$

${\text{\purple{Let}}}\:\:{\purple{(1)+(2)}}$

$\implies 2a-b + 3a+b = 10+5$

$\implies 5a - 0 =15$

$\implies 5a =15$

$\implies a = \frac{15}{5} = 3$

$\boxed {a=3}$

${\text{\purple{To find the value of b substitute a = 3 in (1)}}}$

$\implies 2a-b =10$

$\implies 2(3)-b=10$

$\implies 6-b =10$

$\implies -b =10-6 \implies 4$

$\boxed {b=-4}$

Answer 2

Answer:

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