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**Q1. Find the value of a for which there are infinitely many solutions to the equations**

2x + ay − z = 0

3x + 4y − (a + 1)z = 13

10x + 8y + (a − 4)z = 26

2x + ay − z = 0

3x + 4y − (a + 1)z = 13

10x + 8y + (a − 4)z = 26

Now I know that for there to be infinitely many solutions the determinant of the coefficient matrix must = 0.

I did this on a calculator and found 2 possibilities, 0 and 2.

Additionally, I know that there are infinitely many solutions when 2 of the equations are indentical (by a factor). By trying both 0 and 2 I cannot see how any of the 2 equations will be identical. (Apparently the answer is a=0)

**Q2. Find a value of p for which the system of equations**

3x + 2y − z = 1 and x + y + z = 2 and px + 2y − z = 1

has more than one solution.

3x + 2y − z = 1 and x + y + z = 2 and px + 2y − z = 1

has more than one solution.

Not sure where to start here, more than one solutions hints at what?