System of Linear Equation In Exercises 37-42, use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution.
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Elementary Linear Algebra (MindTap Course List)
- Verify an Equation In Exercises 63-68, evaluate the determinants to verify the equation. |wxyz|=|wx+cwyz+cy|arrow_forwardSolving an Equation In Exercises 49-52, find the values of for which the determinant is zero. |0103222|arrow_forwardSolving an Equation In Exercises 4952, find the value of for which the determinant is zero. |5315|arrow_forward
- Examining Cramer's Rule, explain why there is no unique solution to the system when the determinant of your matrix is O. For simplicity, use a 22 .arrow_forwardVerifying an equation In Exercises 63-68, evaluate the determinants to verify the equation. |1xx21yy21zz2|=(yx)(zx)(zy)arrow_forwardVerifying an Equation In Exercises 63-68, evaluate the determinants to verify the equation. |wxyz|=|yzwx|.arrow_forward
- Finding an Equation of a Line In Exercises 31-36, use a determinant to find an equation of the line passing through the points. 12,3,52,1arrow_forwardUse 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.arrow_forwardnumerical analysis question/Answer according to the system of linear equations given in the picture:a) Arrange in the form AX = B matrix.b) Find the minors and cofactors of each element of the matrix A.c) Find the determinant of the matrix A (with whatever method you want) |A| calculate.arrow_forward
- Use an LU-factorization of the coefficient matrix to solve the follow- ing system of linear equations. x + 2y + z = 1 x + 2y – z 3 x – 2y + z -3.arrow_forwardSolve the system inverse matrix of linear equations x +y = 3z = 2 2x + 3y + 2 = 0 3x + 4y = 2 = 1 using using thearrow_forwardUse the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning