Test your level of competency for GATE Mechanical Engineering for the topic of Linear Algebra from the subject of Engineering Mathematics.

Q1) If A is a matrix such that , find A.

Q2) If  and X is a matrix such that , find X.

Q3) Find an LU factorization of .

Q4) If A is a square matrix whose rows add up to zero vector, then A is

  1. not invertible
  2. invertible
  3. non-singular
  4. cannot say

Q5) Let A be an mxn matrix with linearly independent columns. It is given that  is an invertible matrix. This means that  

  1. need not be invertible
  2. must always be invertible
  3. is a null matrix
  4. none of these

Q6) Linear combination of matrix B as a linear combination of matrices  and  is given by which one of the following options, where,  and 

Q7) If A and B are skew symmetric n x n matrices, then A + B is

  1. also skew symmetric
  2. symmetric
  3. singular
  4. non singular

Q8) If A and B are square matrices and AB is invertible, then A and B are both

  1. invertible
  2. non-invertible
  3. singular
  4. square

Q9) If , find the value of .

Q10) If A is a 3x3 diagonalizable matrix with eigen values -2, 3 and 4, find the value of det(A).


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steps to find the answer for Question 9

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