jee_main_2025_02_april_morning - Matrices and Determinants Topics

Master these core formulas and structures to solve almost any past paper question.

Sample Questions in this Chapter

QUESTION #0 Idempotent Matrices
Let A = beginbmatrix alpha & -1 \\ 6 & beta endbmatrix, alpha > 0, such that det(A) = 0 and alpha + beta = 1. If I denotes the 2 times 2 identity matrix, then the matrix (I + A)^8 is:
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QUESTION #0 System of Linear Equations
If the system of linear equations 3x + y + beta z = 3 2x + alpha y - z = -3 x + 2y + z = 4 has infinitely many solutions, then the value of 22beta - 9alpha is:
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QUESTION #0 Properties of Adjoint
Let a in mathbbR and A be a matrix of order 3 times 3 such that det(A) = -4 and A + I = beginbmatrix 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 endbmatrix, where I is the identity matrix of order 3 times 3. If det((a+1)textadj((a-1)A)) is 2^m 3^n, m, n in \0, 1, 2, dots, 20\, then m+n is equal to:
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)
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