Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 4 down vote favorite

How do I solve these equations with a matrix to get $x$, $y$, and $z$? I'm unsure of how to start.

$$0.09x + 0.10y + 0.12z = 52,000 \\ x + y + z = 500,000 \\ y = 2.5x$$

share|improve this question
2  
$$a x + b y + cz = d \\ e x + f y + g z = h \\ i x + j y + k z = \ell$$ becomes $$ \pmatrix{a & b & c \\ e & f & g \\ i & j & k} \pmatrix{x\\y\\z} = \pmatrix{d \\ h \\ \ell}. $$ – user2468 Sep 11 '12 at 22:31

1 Answer

up vote 2 down vote accepted

First, get rid of the decimals by multiplying the first and third equations by 100.

Next, write the three rows of the matrix A as:

A = {{9, 10, 12}, {1, 1, 1}, {-250, 100, 0}}

Next, write the column matrix for the solution:

b = {5200000, 500000, 0}

Solve by multiplying the inverse of A.b

A^(-1).b = {100000, 250000, 150000}

Verify the answer for each equation and it checks.

HTH

share|improve this answer
I got the same answer! Thank you! – LearningPython Sep 11 '12 at 22:54
1  
Computing $A^{-1}$ is generally considered not to be as good as forming an augmented matrix and doing row reduction. – Gerry Myerson Sep 12 '12 at 2:00

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.