Values

[12] 1. (a) Find an equation of the plane parallel to the lines and and passing through the point P.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) Find the distance between the plane and the line .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Values

[12] 2. Find all values of k such that the system

has no solution. Is there any value of k for which there are infinitely many solutions?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[12] 3. Solve by Gauss-Jordan elimination

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Values

[12] 4. Suppose that A is an invertible matrix such that , where I is the identity matrix. Show that .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[12] 5. (a) Find the inverse of the matrix .

 

 

 

 

 

 

 

 

 

 

 

 

 

(b) Use to solve .