Math+2J+Practice+Midterm+Questions

Math+2J+Practice+Midterm+Questions - 1. Write the...

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Unformatted text preview: 1. Write the coefficient matrix of the following linear system and reduce it to row echelon form. If the system is consistent find all the solutions. +x3 +2x4 = 1 x1 3x1 +2x2 -x3 +4x4 = 5 2. Find the inverse of x2 +2x3 -x4 = 5 2 0 0 A = 1 -3 1 . 5 2 -1 Find the solution of Ax = b in the case 0 2 2 (a) b = 1 (b) b = 0 (c) b = -1 . 1 1 -2 3. Consider the equations x x x +2y +ky +3z +4z =4 =6 +2y +(k + 2)z =6 where k is an arbitrary constant. Determine how many solutions this system has depending on the value of k and justify your answer (you don't have to find the solutions). 4. 3 1 -1 2 0 2 1 3 A= 0 1 3 3 0 1 0 1 a. Compute the determinant of A. b. Is A row equivalent to the 4 4 identity matrix? 5. 2 A= 0 0 0 1 0 1 0 1 Is A diagonalizable? If so find the matrices X (not singular) and D (diagonal) such that A = XDX -1 . If not, then explain why not. 6. Let 2 1 A= s 2 For what values of s R is the matrix A diagonalizable? 1 ...
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