1) Find the inverse using elementary row operation
4X4 [1,1,1,1;1,2,-1,2;1,-1,2,1;1,3,3,2]
2) If A-1 =3X3 [1,1,1;1,1,2;1,-1,1], find A.
3) Which of the following homogeneous system have a nontrivial solution?
2x + z = 0, 2x + 2y + 2z = 0, 4x = 2y = 3z = 0
2x + y - z = 0, x – 2y – 3z = 0, -3x – y + 2z = 0
3x + y + 2z = 0, -2x + 2y = 4z = 0, 2x – 3y + 5z = 0
4) The following system is either in RE form or RRE form. Solve the system using back substitution method.
X + 2y = 2, z + w = -3
5) Consider the linear system
x + 2y + 3z = -1, x – 2y – z = -1, 3x + y + z = 3
Find all the solution by using Gaussian elimination method and Gaussian-Jordan elimination method if it exists.
6) Solve the following systems, with augmented matrix, if it is consistent.
5X4 [1,2,1|7;2,0,1|,4;1,0,2|5;1,2,3|11;2,1,4...
7) Consider the linear system
5x + 2y = a, -15x – 6y = b
Under what conditions (only a and b) if any, does this system fail to have solution.
Does the system have unique solution? Find the unique solution that may exist.
Does the system have infinitely many solutions? Find these solutions if and when they exist.
8) Find a condition on a, b, c that is necessary and sufficient for the system
x – 2y = a, -5x + 3y = b, 3x + y = c
To have a solution.
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