Math+2J+Practice+Midterm

Math+2J+Practice+Midterm - Math 2J Practice Midterm 1....

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Unformatted text preview: Math 2J Practice Midterm 1. Solve the linear system x2 + x3 = 3 3 x1 + 5 x2 + 9 x3 = -2 x1 + 2 x2 + 3x3 = 3 1 4 -3 - 2. Find the inverse of matrix A = 2 -7 6 by the following methods 1 7 -2 (a) Augmented with I 3 and use reduced row echelon form to obtain A-1 (b) Use the formula involving det( A) and adjA . I 0 3. Show that the block matrix is invertible and find its inverse. A I 4. Combine the methods of row reduction and cofactor expansion to compute the determinant of matrix - 1 -4 3 -2 1 3 0 -3 A= 3 4 -2 8 - 3 -4 0 4 5. Use Cramer's rule to compute the solutions of the system 2 x1 + x2 + x3 = 4 - x1 + 2x3 = 2 3 x1 + x2 + 3 x3 = -3 3 1 6 7 - an 3 6. Is 2 eigenvector of 3 7 If so, find the eigenvalue. ? 1 6 5 5 5 -2 7. Find the eigenvalues and eigenvectors of A = . 1 3 8. Chapter 1 Test A (p.87) #3, 6, 8, 10 Test B (p.89) # 4, 5, 12 9. Chapter 2 Test A (p.113) #1, 4, 5, 7, 9 Test B (p.113) # 2 ...
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