5. Solve (for x) the following systems of equations. Note that some of the systems may not have a unique solution: if so, you should state that (with evidence). In all cases, in addition to giving the solution, give the determinant of the coefficient matrix; that is, give det(A), where A is the matrix in the equation Ax = b. (a) ₁₂+3x3 = 3 = 7 2x₁ + x₂ + x3 -3x₁ + x₂ + 4x3 = 0

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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5. Solve (for x) the following systems of equations. Note that some of the systems may not
have a unique solution: if so, you should state that (with evidence).
In all cases, in addition to giving the solution, give the determinant of the coefficient
matrix; that is, give det(A), where A is the matrix in the equation Ax = b.
(a)
(b)
(c)
(d)
3
x1 - x₂ + 3x3
2x1 + x₂ + x3
-3x₁ + x₂ + 4x3 = 0
= 7
2x1 + x2 + x3
−3x1 + x2 + 4x3
21x2 + 3x3
4x13x2 + x3
2x1 + x2 - 4x3
x1 + 2x2 - 2x3
x1 +5x2 + 3x3
5x1 + x2-23
x1 + 2x2 + x3
=
=
=
= -7
= 11
=
-1
= 1
= 1
= 2
= 3
Transcribed Image Text:5. Solve (for x) the following systems of equations. Note that some of the systems may not have a unique solution: if so, you should state that (with evidence). In all cases, in addition to giving the solution, give the determinant of the coefficient matrix; that is, give det(A), where A is the matrix in the equation Ax = b. (a) (b) (c) (d) 3 x1 - x₂ + 3x3 2x1 + x₂ + x3 -3x₁ + x₂ + 4x3 = 0 = 7 2x1 + x2 + x3 −3x1 + x2 + 4x3 21x2 + 3x3 4x13x2 + x3 2x1 + x2 - 4x3 x1 + 2x2 - 2x3 x1 +5x2 + 3x3 5x1 + x2-23 x1 + 2x2 + x3 = = = = -7 = 11 = -1 = 1 = 1 = 2 = 3
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