Engineering

For what values of (¢ belongs to R) the following system of equations has (1)no solution (2)a unique solution (3)infinitely many solutions?
(5-¢)x+4y+2z=4
4x+(5-¢)y+2z=4
2x+2y+(2-¢)z=2

2) Consider three planes in R3. List all possibilities of their intersection. Give example of each case(equations,not diagrams)

3) Let A=|£ ¢| be a
|€ ¥|
matrix and (b vector) belongs to R2. Consider the system represented by AX=b. Then show that
(a) if A is a zero matrix, then any vector (x vector) belongs to R2 is a solution to the system

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