Try out these questions on the topic of Linear Algebra for Engineering Mathematics section in GATE. 

Q1) Determine all 2x2 matrices A, such that AB=BA for any 2x2 matrix B.

Q2) Let  and  be solutions to the homogeneous linear system Ax=0. Then which one of the below given statements are true?

  1.  is a solution
  2.  is a solution
  3. For any scalar, r,  is a solution
  4. For an scalars r and s,  is a solution
  1. only 1
  2. 1,2,3
  3. 2,3 
  4. all of them

Q3) Find a 2x2 matrix  and  such that AB=BA, where . Also find how many such matrices B are there?

Q4) Let  and . Determine all values of 'a' so that the (3,2) entry of LU is 7.

Q5) Find the Square root of the matrix B, where .

Q6) Find a 3x1 matrix with entries not all zero such that, , where .

Q7) Determine the temperatures at the interior points  for the plate shown in the figure below.

Q8) For what values of 'a' does the homogeneous system

(a-1)x+2y=0

2x+(a-1)y=0

has a non trivial solution?

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I didnot solve 2nd and 7th. Thanks for posting Question 2.

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