how to write a matrix A+2B=c as an equation in terms of x ??

Question

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)

Answer 1

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

Answer 2

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