how to write a matrix A+2B=c as an equation in terms of x , where A=(2 -3
-2 5)
and B=(4 3x
0 -1)
and C= (10 -15
-2 3)
how to write a matrix A+2B=c as an equation in terms of x , where A=(2 -3
-2 5)
and B=(4 3x
0 -1)
and C= (10 -15
-2 3)
We have:
A = [2 -3
-2 5]
2B = [8 6x
0 -2]
So A + 2B = [2+8 -3+6x
-2+0 5-2]
or
[10 -3+6x
-2 3]
To rewrite A + 2B = c
[10 (-3+6x) = [10 -15
-2 3] -2 3]
From that we see -3+6x = -15 as an equation in terms of x
So the Matrices are A+2B=C then the first number in A + the first number in B times 2 should = C.
So if you are trying to solve for x you need to note that x in in the top right section of the B matrix, so all of the numbers you are going to use will be in the top right section. that being said use the equation below.
A=-3, B=3x, C=-15. Plug in these numbers to your initial equation of A+2B=C
-3+2(3x) = -15
distribute the 2: -3 + 6x = - 15
Add 3 to both sides: 3-3+6x = -15 + 3 simplify: 6x = -12
get x by itself by dividing both sides by 6: (6x)/6 = -12/6 Simplify:
x=-2
To verify that you have the correct answer plug (-2) in for x in the equation.
-3+2( 3(-2) ) = -15
-3+2(-6) = -15
-3+(-12) = -15 or -3-12 = -15
-15 = -15 Both sides are equal when you plug in our answer for x so x=-2 is correct.
Let me know if you need more help understanding a matrix