Matrices questions
472 published questions with worked solutions.
- Let , ( ) be the values of m, for which the equations x + y + z = 1; x + 2y + 4z = m and x + 4y + 10z = m^2 have infinitely many...
- Let A = [a_ ij ] be a matrix of order 3 × 3, with a_ ij = ( 2 )^ i+j . If the sum of all the elements in the third row of A^2 is...
- Let A be a 3 × 3 real matrix such that A^2(A - 2I) - 4(A - I) = 0, where I and O are the identity and null matrices,...
- Let a ∈ R and A be a matrix of order 3 × 3 such that det(A) = –4 and A + I = bmatrix 1 & a & 1 2 & 1 & 0 a & 1 & 2 bmatrix ,...
- If the system of linear equations 3x + y + βz = 3 2x + αy – z = –3 x + 2y + z = 4 has infinitely many solutions, then the value...
- Let A = bmatrix & -1 6 & bmatrix , α > 0, such that det(A) = 0 and α + β = 1. If I denotes 2 × 2 identity matrix, then the...
- Let I be the identity matrix of order 3 × 3 and for the matrix A = bmatrix & 2 & 3 4 & 5 & 6 7 & -1 & 2 bmatrix , |A| = -1. Let B...
- Let A be a matrix of order 3 × 3 and |A| = 5. If |2 adj (3A adj (2A))| = 2^ .3^ .5^ , , , N, then + + is equal to
- Let A = bmatrix & 0 & - 0 & 1 & 0 & 0 & bmatrix . If for some θ ∈ (0, π), A^2 = A^T, then the sum of the diagonal elements of the...
- Let A = bmatrix 2 & 2+p & 2+p+q 4 & 6+2p & 8+3p+2q 6 & 12+3p & 20+6p+3q bmatrix If det(adj(adj(3A))) = 2^m 3^n, m, n N, then m +...
- Let the system of equations x + 5y – z = 1 4x + 3y – 3z = 7 24x + y + λz = m, λ, μ ∈ **R**, have infinitely many solutions. Then...
- If A is an 3 3 non-singular matrix such that AA' = A'A and B = A^ -1 A', then BB' equals:
- If A = bmatrix 5a & -b 3 & 2 bmatrix and A adj A = AA^T, then 5a + b is equal to
- The system of linear equations x + λy – z = 0 λx – y – z = 0 x + y – λz = 0 has a non-trivial solution for
- If A = bmatrix 2 & -3 -4 & 1 bmatrix , then adj (3A^2 + 12A) is equal to
- Let A = bmatrix 1 & 0 & 0 1 & 1 & 0 1 & 1 & 1 bmatrix and B = A^ 20 . Then the sum of the elements of the first column of B is ?
- Let A = pmatrix & - & pmatrix , (α ∈ R) such that A^ 32 = pmatrix 0 & -1 1 & 0 pmatrix . Then a value of α is:
- If the system of linear equations x - 2y + kz = 1, 2x + y + z = 2, 3x - y - kz = 3 has a solution (x, y, z), z ≠ 0, then (x, y)...
- If bmatrix 1&1 0&1 bmatrix bmatrix 1&2 0&1 bmatrix bmatrix 1&3 0&1 bmatrix bmatrix 1&n-1 0&1 bmatrix = bmatrix 1&78 0&1 bmatrix ,...
- Let α and β be the roots of the equation x^2 + x + 1 = 0. Then for y ≠ 0 in R, vmatrix y+1 & & & y+ & 1 & 1 & y+ vmatrix is equal...
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