anonymous
  • anonymous
Solve the system by using a matrix equation. 2x - 3y = 2 7x - 5y = 7
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jdoe0001
  • jdoe0001
\( \Large \begin{array}{ccc}A&B&X\\ \left[ \begin{array}{lll} 2& -3\\ 7 & -5 \end{array} \right]& \left[ \begin{array}{lll} x\\ y \end{array} \right] & \left[ \begin{array}{lll} 2\\ 7 \end{array} \right] \end{array}\) find the inverse of matrix A and multiply it by the matrix B
jdoe0001
  • jdoe0001
hmm,, rather multiply it by matrix X
anonymous
  • anonymous
I keep getting lost in the process lol. I got the determinant, and start to get the inverse but then I get lost

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anonymous
  • anonymous
@jdoe0001
jdoe0001
  • jdoe0001
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 \(\Large A=\left[ \begin{array}{lll} a&b\\ c& d \end{array}\right], A^{-1} = \frac{1}{D_A}\left[ \begin{array}{lll} d&-b\\ -c& a \end{array}\right]\)
jdoe0001
  • jdoe0001
lost still?
anonymous
  • anonymous
kind of.. lol
jdoe0001
  • jdoe0001
hehe
jdoe0001
  • jdoe0001
so, what's the determinant for the 2x2 matrix A?
anonymous
  • anonymous
-11?
jdoe0001
  • jdoe0001
hmm
jdoe0001
  • jdoe0001
may want to recheck your determinant for \(\large \left[\begin{array}{lll} 2& -3\\ 7 & -5 \end{array} \right]\) I get something else
ybarrap
  • ybarrap
Using Cramer's Rule, http://en.wikipedia.org/wiki/Kramer%27s_rule: $$ |A|=\begin{bmatrix} 2 & -3 \\ 7 &-5 \\ \end{bmatrix}=2(-5)-(-3)(7)=-10+21=11\\ x=\frac{\begin{bmatrix} 2 & -3 \\ 7 &-5 \\ \end{bmatrix}}{|A|}={2(-5)-7(-3)\over 11}={-10+21\over 11}={11\over 11}=1\\ y=\frac{\begin{bmatrix} 2 & 2 \\ 7 &7 \\ \end{bmatrix}}{|A|}={2(7)-2(7)\over 11}=0\\ \text{Answer: }x=1,~y=0 $$

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