Matrices and Determinants
Matrices, algebra of matrices, types of matrices; determinants and matrices of order two and three; properties of determinants; evaluation of determinants; area of triangle using determinants; adjoint and inverse of a matrix; test of consistency and solution of simultaneous linear equations using determinants and matrices.
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Take a full mock →Q1 · Matrices and Determinants · EASY
If A is a 3×3 matrix with |A| = 5, then what is the value of |2A|?
Q2 · Matrices and Determinants · MEDIUM
A square matrix A of order 3 satisfies A^2 - 5A + 7I = O, where I is the identity matrix and O is the null matrix. If A is non-singular, what is A^(-1) equal to?
Q3 · Matrices and Determinants · MEDIUM
The system of equations x + 2y + 3z = 1, 2x + 3y + 4z = 3, 3x + 4y + 5z = k has infinitely many solutions. What is the value of k?
Q4 · Matrices and Determinants · EASY
If the area of a triangle with vertices (1, 2), (3, 5), and (4, k) is 5 square units, then which of the following can be a value of k?
Q5 · Matrices and Determinants · HARD
Let A be a 3×3 skew-symmetric matrix. If B = I + A and C = I - A, where I is the identity matrix of order 3, and if C is invertible, then which of the following equals BC^(-1)?