In Exercises 1–8, solve the system by inverting the coefficient matrix and using Theorem 1.6.2.
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- In Exercises 29–32, find the elementary row operation that trans- forms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.arrow_forwardIn Exercises 11–14, find parametric equations for all least squares solutions of Ax = b, and confirm that all of the solutions have the same error vector. 1 3 1 12. A = -2 -6 |; b = ! 0 3 9. 1arrow_forwardFind the determinants in Exercises 5–10 by row reduction to echelon form. just number 7arrow_forward
- In 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_forwardIn Exercises 11–16, compute the adjugate of the given matrix, and then use Theorem 8 to give the inverse of the matrix.arrow_forwardQ4: If the matrix A = Show that A2 - 2A – 21 = 0.arrow_forward
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