Find a and b to make the following matrices equal. \left[\begin{array}{ccc}a+2b&4\\2&a+4\\1&0\end{array}\right] \left[\begin{array}{ccc}-a&4\\2&2a-3b\\1&…

Question

Find a and b to make the following matrices equal.


`\left[\begin{array}{ccc}a+2b&4\\2&a+4\\1&0\end{array}\right]` 
`\left[\begin{array}{ccc}-a&4\\2&2a-3b\\1&0\end{array}\right]`

Thanks :)

Answer 1

Each spot in the matrix should equal the same spot in the other matrix. See how the constants match up?

So then you have two equations for the two spots with a' and b's.
a + 2b = -a
a + 4 = 2a - 3b

That first equation tells us that b = -a
a + 2b = -a
2b = -2a
b = -a

Sub -a in for b in the other equation.

a + 4 = 2a - 3(-a)
a + 4 = 2a + 3a
a + 4 = 5a
4 = 5a - a
4 = 4a

a = 1
then b = -1

Answer 2

We need the following to be true
a+2b = -a
a+4 = 2a - 3b

Let's look at the first equation.
a + 2b = -a
Subtract both sides by a
2b = -2a
b = -a

Substitute b= -a into the second equation
a+4 = 2a + 3a
a + 4 = 5a
4a = 4
a = 1

Just take the negative of that and you get the value of b.
b = -1

Your solution is a=1 and b = -1.

Have an awesome day! :)