In each of Problems 2 through 5, if there exist solutions of the homogeneous system of linear equations other than
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- Solve each of the following systems: x+ 2y – 4z = -4 2x + 5y – 9 = –10 3x – 2y + 3z = 11 (a) x+ 2y – 3z = 1 2x + 5y – 8z = 4 Зх + 8y — 13г 3 7 (c) x+ 2y – 3z = -1 — Зх + у - 2г — -7 5x + 3у — 42 — 2 (b) Reduce each system to triangular or echelon form using Gaussian elimination: (a) Apply “Replace L, by -21, + L," and "Replace L, by -3L +L;" to eliminate x from the second and third equations, and then apply "Replace Lz by 812 + Lz" to eliminate y from the third equation. These operations yield x + 2y - 42 = -4 2= -2 x+ 2y – 4z = -4 y - z= -2 7z = 7 y- and then -8y + 15z = 23 The system is in triangular form. Solve by back-substitution to obtain the unique solution и 3 (2, -1,1). (b) Eliminate x from the second and third equations by the operations "Replace L2 by 3L1 + L," and "Replace Lz by –5L, + Lz." This gives the equivalent system x+ 2y - 3z = -1 7y – 11z = - 10 7 -7y + 11z = The operation "Replace Lz by L2 + L,'" yields the following degenerate equation with a nonzero constant: Ox…arrow_forwardWrite the following system as a vector equation involving a linear combination of vectors and solve for the unknowns. 5x12x2x3 = 2 4x₁ + 3x3 = −1arrow_forwardSolve the following system of linear equations: x₁+x2-x3 = -1 -x₁+2x2-8x3 = 4 3x1+4x2-6x3 = −1 If the system has no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system. If the system has infinitely many solutions, select "The system has at least one solution". Your answer may use expressions involving the parameters r, s, and t. You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. The system has no solutions Row-echelon form of augmented matrix: The system has no solutions The system has at least one solution 0 0 0 000 0 0 0arrow_forward
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