Question

If matrix (a b) =-2
(c d)

then find
(6a-2b 3c-d )
(2d 4b )
​

Answer 1

Answer:

Can it be solved: a+b=8;c−d=6;a+c=13;b+d=8 ?

Season to start anew.

Let’s rearrange the first and third equations in terms of a :

⇒a+b=8⇒a=8−b (i)

and

⇒a+c=13⇒a=13−c(ii)

Then, let’s equate (i) and (ii) :

⇒8−b=13−c⇒b=c−5(iii)

Now, let’s use the second and fourth equations to find expressions for b and c :

⇒c−d=6⇒c=6+d(iv)

and

⇒b+d=8⇒b=8−d(v)

Let’s equate (iii) and (v) :

⇒c−5=8−d⇒c=13−d(vi)

We can now equate (iv) and (vi) :

⇒6+d=13−d⇒2d=7∴d=72

Let’s substitute this value of d into (iv) and (v) :

∴c=6+(72)=192

and

∴b=8−(72)=92

We can use either (i) or (ii) to find a .

Let’s try using (i) :

∴a=8−(92)=72

Therefore, the solutions to the system of equations is a=72 , b=92 , c=192 , and d=72 .

Step-by-step explanation:

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