How would you solve the following system of linear equations: 2x_1 + (3+a)x_2 + 2x_3 = 2+aZ

Margaux Cole 2022-02-22 Answered
How would you solve the following system of linear equations:
2x1+(3+a)x2+2x3=2+a
x1+ax2+2x3=a
ax1+2x2+2ax3=0
assuming that a±2? I feel confident in solving linear equation systems with just constants as the coefficients but the variable coefficient a is what gives me problems.
Here is the solution I find: solution as augmented matrix but how would the assumption about a make the reduced echelon form any different compared to an assumption about e.g.a±2?
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Expert Answer

Balraj Conrad
Answered 2022-02-23 Author has 9 answers
With
x1=aax22x3
can we eliminate x1:
x2(3a)2x3=2a
x2(2a2)+4ax3=a2
And then using
x3=x2(3a)(2a)2
to eliminate x3. Then you will get
x2(2a2)+2a(3a)x22a(2a)=a2
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