Question

[1 -2
3 x]
For what value of x in this matrix is there no inverse?

Answer 1

Hint: consider the matrix\[\left[ \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] \right]\]

Answer 2

If ab = cd, the matrix does not have an inverse (due to division by zero).

Answer 3

Use this fact to determine the value of x.

Answer 4

I'm sorry, I still don't understand.

Answer 5

u still need help?

Answer 6

yes please

Answer 7

ok remember a metrix does not have an inverse if the determinant is equal to 0 right?

Answer 8

Right

Answer 9

now to elaborate more on what mathmale had stated above.. If ab = cd, the matrix does not have an inverse. in your case
1 times x=?
3 times -2=-6
so then 1 times -6=-6

Answer 10

now try to find the determinant what do you get

Answer 11

so x=-6 ?

Answer 12

yes

Answer 13

u know how to find the determinant?

Answer 14

yes I do, I found the determinant is 0 so that means x=-6. So the main goal is to get the determinant to equal 0?

Answer 15

yes

Answer 16

Note that "ad=bc" is equivalent to "the determinant is 0."

Answer 17

okay thank you!

Answer 18

magepker728, your clarifications were very good.

Answer 19

thanks @mathmale