Question

Determine whether the matrix has an inverse. If an inverse exists, find it.(pic attached)

Answer 1

first check the determinant, if it is not zero, matrix has an inverse
we can find the inverse of a two by two matrix easily

Answer 2

k then what

Answer 3

\[A=\left| \begin{array}{cc} a & b \\ c & d \end{array} \right|\]
\[A^{-1}=\frac{1}{ad-bc} \left|\begin{array}{cc} d & -b \\ -c & a\end{array} \right|\]

Answer 4

you can see why you need the determinant to be non- zero , because you have to divide by it

Answer 5

i got [7 18
[-2 5]

Answer 6

in your case the determinant is one right?

Answer 7

i think so

Answer 8

\[ad-bc=-5\times 7-(-18)\times 2=-35+36=1\] is what i get

Answer 9

so we don't have to worry about dividing by anything
you have a mistake in your answer however

Answer 10

whats the final answer then

Answer 11

last entry should be -5, not 5

Answer 12

\[A^{-1}=\left| \begin{array}{cc} 7 & 18 \\ -2 & -5 \end{array} \right|\]

Answer 13

maybe that was a typo on your part. don't change the sign of \(a\) and \(d\), just switch them

Answer 14

k

Answer 15

thanks

Answer 16

yw