In Problems 1–6 write the given linear system in matrix form.
9.
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- 3. Suppose we have a matrix A = 1 1 101 1 2 2 What is rank of A?arrow_forwardProblem 13. Write the matrix M = where Then z = (a) 1 (b) 2 (c) 3 (d) 4 A 13 24 as a linear combination of the form M = A + B + zC, 8 B= ---- and C=arrow_forward9. (a) Evaluate the matrix product Ax, where A = 1. and x = 3 Hence show that the system of linear equations 7x + 5y = 3 x + 3y = 2 can be written as Ax b where b = %3D (b) The system of equations 2r + 3y – 2z = 6 x– y + 2z = 3 4x + 2y + 5z = 1 can be expressed in the form Ax = b. Write down the matrices A, x and b.arrow_forward
- 2. Find the solution set to the following system of linear equations using Gauss-Jordan elimination. (2.x1 + 7x2 – 12.x3 = -9 x1 + 2x2 – 3.x3 = 0 3x1 + 5x2 – 7x3 = 3 - Determine the rank of the coefficient matrix and the augmented matrix.arrow_forward1.2. Find a matrix A for which a1,1 = a2,2 = a3,3 = 1, but elimination (with no row exchanges) produces two negative pivots (the first pivot is 1).arrow_forwardSolving Systems Use Gauss-Jordan reduction to transform the augmented matrix of each system in Problems 24–36 to RREF. Use it to discuss the solutions of the system (i.e., no solutions, a unique solution, or infinitely many solutions). 74 + 25 - - 2 29. x₁ + 4x₂ = 5x3 = 0 2x1x2 + 8x3 = 9arrow_forward
- 3arrow_forward7. Let A be a matrix with a row consisting of all zeroes. If B is a matrix such that AB is defined, which of the following is always true? 8. Given the matrix B = 1 1 11 Which of the following (233) (a) 3 2 3 332 matrices solves X in the matrix equation X+13= 2(X - B)? (211) (d) 1 2 1 112 (322) (b) 2 3 2 2 2 3 (122) (c) 2 1 2 2 2 1arrow_forward18. Find all a and ß > 0 so that the matrix 4 1 A = 28 5 4 %3D 2arrow_forward
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