In Exercises 5–14, the matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists.
14.
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- In Exercises 7–10, the augmented matrix of a linear system has been reduced by row operations to the form shown. In each case, continue the appropriate row operations and describe the solution set of the original system. 1 7 3 -4 1 -4 1 -1 3 7. 8. 1 7 1 1 -2 0 -4 0 -7 1 -1 1 -3 9. 1 -3 -1 4arrow_forward2. Solve for x in the given matrix equalitiesarrow_forwardConvert the augmented matrix [5 -3 4 2 || || -3 0 -5 to the equivalent linear system. Use x1, x2, and x3 to enter the variables x₁, x2, and x3. 8:8arrow_forward
- Determine the cofactor of 2 in the matrix A = 3 7. 4 -4 3. -3arrow_forward2 5 31 5. Write X =|-3 6 0 as the sum of a skew symmetric and a symmetric 4 1 1] matrix.arrow_forward5. By using the matrix methods to solve the following linear system: I1 + 12 – 13 = 5, 3r1 +x2 – 2r3 = -4, -I1 + 12 - 2r3 = 3;arrow_forward
- Find a system of linear equations corresponding to the augmented matrix. 505 65-5 06 9 x₁ + i X₁+ i x₁ + x₂ = 5 x2 = -5 x₂ = 9arrow_forward1. Let a = (5, –8,0, 3) and b = (0, 2, –4, 3). (a) Calculate (2b – 4a) (b) Calculate (2b — 4а) (b + 2а) (c) Calculate || a || and || b || (d) Show that the Triangle Inequality applies in this case. 2. Consider the following matrix: -2 1 3 A = 4. 1 -2 -1 (a) Calculate the determinant of A. (b) Find the inverse of A, if it exists. 3. Solve the following system of linear equations using matrix inversion: -2x + y + 3z = 11 4л + 5у + 32 %3 3 I - 2y – z = -6arrow_forwardIn Exercises 1–4, determine if the system has a nontrivial solution. Try to use as few row operations as possible.arrow_forward
- 3. Let A be a 4 × 4 matrix. Suppose the matrix equation A = has solution set 1 what is the solution set of A = 0? 2.arrow_forwardSolve the following linear equations using the 5 methods: (Gaussian Elimination, Gauss-Jordan Elimination, LU Factorization, Inverse Matrix and Cramer's Rule). Show your complete solutions. b. 2x1 — 6х, — Хз 3D — 38 -3x1 – x2 + 7x3 = -34 -8x1 + x2 – 2x3 = -20arrow_forwardSLOVE THE SYSTEM BY GAUSSarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage