If  and the reduced row echelon form of is , then

A quadratic polynomial of the form passes through (1,1), (2,2) and (3,5). 

Which of the following represents the correct matrix equation for the linear system to find ?

For the following linear system, determine whether the following statements are true or false.

Here, is a real constant.

Suppose that , and are matrices with the following sizes:

Determine whether the given matrix expression is defined.

Find the solution of the following system by using LU decomposition. 

(If you do not use LU decomposition, you will not get any score.)

Let , and . Find X if 

For which value(s) of , is the following matrix invertible?

Suppose that and are invertible matrices. If and , determine whether the following is true or false.

Consider the matrices 

Suppose that . Find .

For which value of the homogeneous system has infinitely many solutions?