Question

please solve this question ✌
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Answer 1

Answer:

Step-by-step explanation:

$\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$ × $\left[\begin{array}{ccc}f&g\\h&j\end{array}\right]$ = $\left[\begin{array}{ccc}af+bh&ag+bj\\cf+dh&cg+dj\end{array}\right]$

~~~~~~~~~~~~~~~~

(i).

$\left[\begin{array}{ccc}a-b&b-4\\b+4&a-2\end{array}\right]$ × $\left[\begin{array}{ccc}2&0\\0&2\end{array}\right]$ = $\left[\begin{array}{ccc}-2&-2\\14&0\end{array}\right]$

2(a - b) + 0(b - 4) = - 2 ⇒ a - b = - 1

2(b + 4) + 0(a - 2) = 14 ⇒ b + 4 = 7 ⇒ b = 3

a - 3 = - 1 ⇒ a = 2

Check the answer:

$\left[\begin{array}{ccc}-1&-1\\7&0\end{array}\right]$ × $\left[\begin{array}{ccc}2&0\\0&2\end{array}\right]$ = $\left[\begin{array}{ccc}-2&-2\\14&0\end{array}\right]$

$\left[\begin{array}{ccc}-2&-2\\14&0\end{array}\right]$ = $\left[\begin{array}{ccc}-2&-2\\14&0\end{array}\right]$

(ii).

$\left[\begin{array}{ccc}8&-2\\1&4\end{array}\right]$ × X = $\left[\begin{array}{ccc}12\\10\end{array}\right]$

$\left[\begin{array}{ccc}8&-2\\1&4\end{array}\right]$ × $\left[\begin{array}{ccc}x_{1} \\x_{2} \end{array}\right]$ = $\left[\begin{array}{ccc}12\\10\end{array}\right]$

8 $x_{1}$ + ( - 2) $x_{2}$ = 12

$x_{1}$ + 4 $x_{2}$ = 10

$x_{1}$ = 10 - 4 $x_{2}$

8 ( 10 - 4 $x_{2}$ ) - 2 $x_{2}$ = 12

- 34 $x_{2}$ = - 80 + 12

- 34 $x_{2}$ = - 68

$x_{2}$ = 2

$x_{1}$ = 2

X = $\left[\begin{array}{ccc}2\\2\end{array}\right]$

Answer 2

Answer:

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