In Exercises 1–24, use Gaussian elimination to find the complete solution to each system of equations, or show that none exists.
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- In Exercises 5–8, use the definition of Ax to write the matrix equation as a vector equation, or vice versa. 5. 5 1 8 4 -2 -7 3 −5 5 -1 3 -2 = -8 - [18] 16arrow_forwardIn Exercises 7–10, the augmented matrix of a linear system hasbeen reduced by row operations to the form shown. In each case,continue the appropriate row operations and describe the solutionset of the original systemarrow_forwardIn Exercises 5–8, use the definition of to write the matrix equation as a vector equation, or vice versa.arrow_forward
- Find the determinants in Exercises 5–10 by row reduction to echelon form.arrow_forwardIn Exercises 1–4, determine if the system has a nontrivial solution. Try to use as few row operations as possible.arrow_forwardSection 2.2 2.1. Solve the following difference equations: (a) Yk+1+Yk = 2+ k, (b) Yk+1 – 2Yk k3, (c) Yk+1 – 3 (d) Yk+1 – Yk = 1/k(k+ 1), (e) Yk+1+ Yk = 1/k(k+ 1), (f) (k + 2)yk+1 – (k+1)yk = 5+ 2* – k2, (g) Yk+1+ Yk = k +2 · 3k, (h) Yk+1 Yk 0, Yk = ke*, (i) Yk+1 Bak? Yk (j) Yk+1 ayk = cos(bk), (k) Yk+1 + Yk = (-1)k, (1) - * = k. Yk+1 k+1arrow_forward
- In Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forwardIn Exercises 13–17, determine conditions on the bi ’s, if any, in order to guarantee that the linear system is consistent. 13. x1 +3x2 =b1 −2x1 + x2 =b2 15. x1 −2x2 +5x3 =b1 4x1 −5x2 +8x3 =b2 −3x1 +3x2 −3x3 =b3 14. 6x1 −4x2 =b1 3x1 −2x2 =b2 16. x1 −2x2 − x3 =b1 −4x1 +5x2 +2x3 =b2 −4x1 +7x2 +4x3 =b3 17. x1 − x2 +3x3 +2x4 =b1 −2x1 + x2 + 5x3 + x4 = b2 −3x1 +2x2 +2x3 − x4 =b3 4x1 −3x2 + x3 +3x4 =b4arrow_forwardFind a 2 × 2 matrix that maps e₁ to -3e2 and e2 to 2e1–e2.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage