Linear Algebra Questions

Solve on Page.

81: Without directly evaluating, show that 2 = ? satisfy 2 2 3 O - 5Q2: Solve the system of equations by Crout's method 4 + lon + 3 = 12 2# + 104 + 3 = 13 24 + 2x + 103 = 14 Q3. Verify AB= BA for the following matrices A = cos - Sinox B= / cost - sin8 sina COSA sin 8 costQ4: Use an inverse matrix ( by Gauss Jordan Elimination ) to solve the system 271 + 34 + 3 = - 1 3 x + 3 1 + 3 = 1 2* + 4 4 + 3 = - 2. 25: Let A = [ 1 2 ( Note: Calculate A by Gauss Jordan Elimination -2 1 a ) show that A2 - 2A + 51 = 0, where I is -the identity matrix and O is zero matrix of order 2. b ) Show that A - 1 (21-A) 5Q6: Using elementary row operations to evaluate the determinant ( i ) - 3 4 lu ) - 2 7 - 4 5 3 3 6 - 5 3 2 3 - 1 - 3 - 1 - 4 -2 - 1