Consider the following system of equations: x1 + 2x2 + 3x3 = a x1 - x2 = b x2 +

Question

Consider the following system of equations:
x1 + 2x2 + 3x3 = a
x1 - x2 = b
x2 + 4x3 = c

For which values of a, b, & c is the system consistent? This question is from the very first chapter of a linearalgebra course, so the techniques required to answer the questionshould not be extremely advanced. I believe we are supposed to addor subtract multiples of the equations until we arrive at anequation in the form 0=(some combination of a, b, and c). Then, wecan state that the system is consistent for any values of a, b, andc that make the combination of a, b, and c from the equation equalto zero. For example, if we arrive at 0=2a-b+c, then the answerwould be any values of a, b, and c whereby 2a-b+c=0. The problemI'm facing is arriving at this equation. :(


Thanks for your help! Consider the following system of equations:
x1 + 2x2 + 3x3 = a
x1 - x2 = b
x2 + 4x3 = c

For which values of a, b, & c is the system consistent? This question is from the very first chapter of a linearalgebra course, so the techniques required to answer the questionshould not be extremely advanced. I believe we are supposed to addor subtract multiples of the equations until we arrive at anequation in the form 0=(some combination of a, b, and c). Then, wecan state that the system is consistent for any values of a, b, andc that make the combination of a, b, and c from the equation equalto zero. For example, if we arrive at 0=2a-b+c, then the answerwould be any values of a, b, and c whereby 2a-b+c=0. The problemI'm facing is arriving at this equation. :(


Thanks for your help!

Explanation / Answer

Have you learned any methods yet such as Gauss or Gauss-Jordan (akarow echelon)?

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