MATH 2264-005: Matrices and Linear Algebra Practice Problems for Exam 1 1. Do the lines 2x + 3y = 1 and x + 4y = 3 have a common point of intersection? 2. Describe the solution set in of 2x1 + 3x2 2x3 = 2 in parametric form. 3. Describe the solution set of x1 3x2 + 4x3 = 2 2x1 + x2 2x3 = 3 in parametric form. 4. Describe the solution set of 3x1 + 2x2 x3 = 7 x1 2x2 + 3x3 = 1 2x1 2x2 + 2x3 = 3 in parametric form. 5. For which values of h is the system consistent? For which valued is the solution unique? x1 x2 = 4 2x1 + 3x2 = h 6.For which values of h and k does the system have a) no solution, b) a unique solution, c) many solutions. x1 + hx2 = 2 4x1 + 8x2 = k 7. Let 2 3 4 b1 A = 2 1 2 , b = b2 4 2 4 b3 Show that the equation Ax = b is not consistent for all possible b. For which b is it consistent? 1 8. Let 7 2 5 8 5 3 4 9 A= 6 10 2 7 7 9 2 15 Do the columns of the matrix A span R4? 9. Problems 5 on page 48. 10. Problems 5, 7, 13, 15, and 17 on page 61-62. 11. Show that the transformation T : R2 7 R2 \u0012 T (x) = x21 3x2 2x1 7x2 is not linear. 12. Pages 79-80 #5, 9, 17, 25 2 \u0013 Scanned by CamScanner Scanned by CamScanner