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Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution. 3x1 + x2 + 4x3 + x4 = 7 4x4 = -2 X1 + X2 3x3 2x1 + 7x2 + 2x3 3x4 = 8 X1 + 5x₂ 6x3 = 4 O The system has a unique solution because the determinant of the coefficient matrix is nonzero. O The system has a unique solution because the determinant of the coefficient matrix is zero. O The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. O The system does not have a unique solution because the determinant of the coefficient matrix is zero.

Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution. 3x1 + x2 + 4x3 + x4 = 7 4x4 = -2 X1 + X2 3x3 2x1 + 7x2 + 2x3 3x4 = 8 X1 + 5x₂ 6x3 = 4 O The system has a unique solution because the determinant of the coefficient matrix is nonzero. O The system has a unique solution because the determinant of the coefficient matrix is zero. O The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. O The system does not have a unique solution because the determinant of the coefficient matrix is zero.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.2: Multiplicative Inverses
Problem 41PS
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Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution. 3x1 + x2 + 4x3 + X₁ + X2 - 3x3 2x₁ + 7x2 + 2x3 X1 + 5x₂ 6x3 X4 = 7 4x4 = -2 3x4 = 8 = 4 O The system has a unique solution because the determinant of the coefficient matrix is nonzero. O The system has a unique solution because the determinant of the coefficient matrix is zero. O The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. O The system does not have a unique solution because the determinant of the coefficient matrix is zero.
Transcribed Image Text:Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution. 3x1 + x2 + 4x3 + X₁ + X2 - 3x3 2x₁ + 7x2 + 2x3 X1 + 5x₂ 6x3 X4 = 7 4x4 = -2 3x4 = 8 = 4 O The system has a unique solution because the determinant of the coefficient matrix is nonzero. O The system has a unique solution because the determinant of the coefficient matrix is zero. O The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. O The system does not have a unique solution because the determinant of the coefficient matrix is zero.
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