How to solve this?

Question

x₁ + 2x₂ + x₃ + x₄+ 5x₅ = 0

−5x₁ + 10x₂ + 3x₃+ 3x₄+ 55x₅ = −8

x₁+ 2x₂ + 2x₃ − 3x₄ − 5x₅= 14

−x₁− 2x₂+ 6x₃ − 12x₄ + 8x₅= −2

(a) Determine whether the non-homogeneous system Ax = b is consistent.

Answer 1

x₅ will be "free" variable

since system is 4 equations with 5 variables..

Use Gauss-Jordan elimination

and if the last row has x₄ equal to a linear function of x₅

then system consistent.

If any row has 0=constant then system is inconsistent.

obviously a determinate of the matrix does not exist since it is a 4x5 matrix.

Answer 2

Hey,

The simplest way to solve this system of equations would be to use matrix math(linear algebra). Are you familiar with how to do this on a calculator?