Question

find the
2 1]
If A =
and B =
1 3
matrix X such that AX = B.
L-11
solve it plz .​

Answer 1

Answer:

Don't know the answer expecting from someone else.

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \underline{ \underline{{ \huge{ \textbf{ \textsf{M}}}}{ \tt{ATRIX \: \: \: }}}}}$

$\underline{ \underline{{ \huge{ \blue{ \mathfrak{Q}}}}{ \bold{ \green{UES}}}{ \red{ \bold{TION -}}}}}$

${\tt{If \: A = \left[ \begin{array}{c c } \sf 2& \sf 1\\\\ \sf \: 1& \sf \: 3 \end{array} \right] and \: B = \left[ \begin{array}{c c } \sf 3\\\\ \sf \: -11 \end{array} \right];}}$

find the matrix X such that AX = B.

$\underline{ \underline{{ \huge{ \blue{ \mathfrak{A}}}}{ \bold{ \green{NS}}}{ \red{ \bold{WER -}}}}}$

${\tt{A = \left[ \begin{array}{c c } \sf 2& \sf 1\\\\ \sf \: 1& \sf \: 3 \end{array} \right]_{2×2}}} \\\\{ \tt{ B = \left[ \begin{array}{c } \sf 3\\\\ \sf \: -11 \end{array} \right]_{2 \times 1}}}$

${\tt{Let \: X = \left[ \begin{array}{c } \sf a \\\\ \sf b \end{array} \right]}}$

AX = B

$\implies{\tt{ \left[ \begin{array}{c c } \sf 2& \sf 1\\\\ \sf \: 1& \sf \: 3 \end{array} \right] \left[ \begin{array}{c } \sf a \\\\ \sf b \end{array} \right] = \left[ \begin{array}{c } \sf 3\\\\ \sf \: -11 \end{array} \right]}} \\\\\\ \implies{\tt{\left[ \begin{array}{c } \sf 2a + b\\\\ \sf \: a + 3b \end{array} \right] = \left[ \begin{array}{c } \sf 3\\\\ \sf \: -11 \end{array} \right] }} \\\\\\ \implies{\tt{ 2a + b = 3 \: \: \: ...(i) ×3}}</p><p>\\ \implies{\tt{a + 3b = -11 \: \: \: ...(ii) ×1 }}$

6a + 3b = 9

a + 3b = -11

(-) (-) (-)

__________

5a = 20

a = 20/5

$\boxed{{\tt{\therefore \: a = 4}}}$

On putting the value of a in eq. (i)

↠2a + b = 3

↠2 × 4 + b = 3

↠8 + b = 3

↠b = 3 - 8

$\boxed{{\tt{\therefore \: b = -5}}}$

${\tt{\therefore \: X = \left[ \begin{array}{c } \sf a \\\\ \sf b \end{array} \right] = \red{ \left[ \begin{array}{c } \sf 4 \\\\ \sf -5 \end{array} \right] \: \: \: \: ans.. \: }}}$

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