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).

steps to find the answer for Question 9

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@SANJAY DAS  yes

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