GUJCET Matrices and Determinants — practice questions
27 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice GUJCET Matrices and Determinants in the app →A matrix is:Identity matrix I has:For matrix multiplication AB to be defined:Determinant of 2×2 matrix [[a, b], [c, d]]:Determinant of triangular (upper or lower) matrix:A matrix is invertible iff:For 2×2 matrix A = [[2,3],[1,4]], A⁻¹ =Transpose of [[1,2,3],[4,5,6]] is:For matrices A, B (square, same size): (AB)^T =A matrix is symmetric if:A matrix is skew-symmetric if:Determinant of identity matrix I_n:Determinant: if two rows are equal, det =For matrix A with |A| = 5 and A is 3×3, |2A| =For matrix A and its adjugate adj(A): A × adj(A) =For non-singular A and scalar k: |k A^(-1)| = (A is n × n)Solve: x + y + z = 6, 2x + y - z = 1, x - y + z = 2. Determinant of coefficient matrix:If A is orthogonal (A A^T = I), then |A| =For A = [[3, 1], [2, 4]], characteristic polynomial:Eigenvalues of A = [[3,1],[2,4]]:For matrix A, rank(A) + nullity(A) =For A symmetric n×n matrix, all eigenvalues are:Trace of matrix is sum of diagonal entries. For 2×2 [[a,b],[c,d]]:System of equations Ax = b has unique solution iff:For 3×3 matrix with rows R₁, R₂, R₃ = R₁ + 2R₂. Determinant =If A is 3×3 with |A| = -2, then |adj(A)| =Product of eigenvalues of square matrix A =