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
- not invertible
- cannot say
Q5) Let A be an mxn matrix with linearly independent columns. It is given that is an invertible matrix. This means that
- need not be invertible
- must always be invertible
- is a null matrix
- 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
- also skew symmetric
- non singular
Q8) If A and B are square matrices and AB is invertible, then A and B are both
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).