Question

Solve the system by using a matrix equation.
2x - 3y = 2
7x - 5y = 7

Answer 1

\( \Large \begin{array}{ccc}A&B&X\\
\left[
\begin{array}{lll}
2& -3\\
7 & -5
\end{array}
\right]&
\left[
\begin{array}{lll}
x\\
y
\end{array}
\right] &
\left[
\begin{array}{lll}
2\\
7
\end{array}
\right]
\end{array}\)

find the inverse of matrix A and multiply it by the matrix B

Answer 2

hmm,, rather multiply it by matrix X

Answer 3

I keep getting lost in the process lol. I got the determinant, and start to get the inverse but then I get lost

Answer 4

@jdoe0001

Answer 5

ahemm, well, to get the inverse, you will need the inverse determinant anyhow, keep in mind that for a 2x2 matrix, the inverse can be obtained by \(\Large A=\left[
\begin{array}{lll}
a&b\\
c& d
\end{array}\right],
A^{-1} = \frac{1}{D_A}\left[
\begin{array}{lll}
d&-b\\
-c& a
\end{array}\right]\)

Answer 6

lost still?

Answer 7

kind of.. lol

Answer 8

hehe

Answer 9

so, what's the determinant for the 2x2 matrix A?

Answer 10

-11?

Answer 11

hmm

Answer 12

may want to recheck your determinant for \(\large \left[\begin{array}{lll}
2& -3\\
7 & -5
\end{array}
\right]\) I get something else

Answer 13

Using Cramer's Rule, http://en.wikipedia.org/wiki/Kramer%27s_rule:
$$
|A|=\begin{bmatrix}
2 & -3 \\
7 &-5 \\
\end{bmatrix}=2(-5)-(-3)(7)=-10+21=11\\
x=\frac{\begin{bmatrix}
2 & -3 \\
7 &-5 \\
\end{bmatrix}}{|A|}={2(-5)-7(-3)\over 11}={-10+21\over 11}={11\over 11}=1\\
y=\frac{\begin{bmatrix}
2 & 2 \\
7 &7 \\
\end{bmatrix}}{|A|}={2(7)-2(7)\over 11}=0\\
\text{Answer: }x=1,~y=0
$$