Question

solve the following matrix equation for a, b, c, d.

[a - b b + c ] = [8 1]
[3d + c 2a - 4d] [7 6]

the ans :

a = 5
b = -3
c = 4
d = 1

Answer 1

please help

Answer 2

so we have
a-b=8 (eq1) b+c=1 (eq2)
3d+c=7 (eq3) 2a-4d=6 (eq4)
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from the first equation we can write a=8+b
We can plug this into equation 4 2(8+b)-4d=6 => 16+2b-4d=6
=> 2b-4d=6-16
=> 2b-4d=-10
=> b-2d=-5
=> b=-5+2d
We can plug this into equation 2 (-5+2d)+c=1=>2d+c=6
=> c=6-2d
Finally plug this into equation 3 and solve for d

Answer 3

is that the answer?

Answer 4

no

Answer 5

that will give you what d is

Answer 6

but we haven't found all the other values a,b, and c

Answer 7

i see

Answer 8

how does a - b = 8 turn into a = 8 + b?

Answer 9

ok nvm dumb question

Answer 10

so I said c=6-2d and i asked you to plug this into equation 3 and equation 3 was
3d+c=7 (eq3)
which gives 3d+(6-2d)=7
6+d=7
=> d=1

Answer 11

ok

Answer 12

I think i can get the rest

Answer 13

THANK YOU VERY MUCH

Answer 14

ok cool!