Matrices questions
472 published questions with worked solutions.
- Let A = bmatrix 1 & 2 0 & 1 bmatrix and B = I + adj(A) + (adj A)² + … + (adj A)^ 10 . Then, the sum of all the elements of the...
- Let A be a 2 × 2 symmetric matrix such that A bmatrix 1 1 bmatrix = bmatrix 3 7 bmatrix and the determinant of A be 1. If A⁻¹ =...
- Let A and B be two square matrices of order 3 such that |A| = 3 and |B| = 2. Then |Aᵀ A (adj(2A))⁻¹ (adj(4B)) (adj(AB))⁻¹ A Aᵀ|...
- The values of m, n, for which the system of equations x + y + z = 4, 2x + 5y + 5z = 17, x + 2y + mz = n has infinitely many...
- For which of the following ordered pairs ( , ), the system of linear equations x+2y+3z=1 3x+4y+5z= 4x+4y+4z= is inconsistent ?
- The number of all 3 × 3 matrices A, with enteries from the set –1, 0, 1 such that the sum of the diagonal elements of AA^T is 3,...
- Let a, b, c R be all non-zero and satisfy a^3+b^3+c^3=2. If the matrix A= pmatrix a&b&c &c&a &a&b pmatrix satisfies A^TA=I, then...
- Let A= X=(x,y,z)^T: PX=0 and x^2+y^2+z^2=1 where P= pmatrix 1&2&1 -2&3&-4 1&9&-1 pmatrix , then the set A :
- If A is a square matrix of order 3 such that det(A) = 3 and det(adj(−4 adj(−3 adj(3 adj((2A)⁻¹))))) = 2ᵐ3ⁿ, then m + 2n is equal...
- Let S be the set of all R for which the system of linear equations 2x-y+2z=2 x-2y+ z=-4 x+ y+z=4 has no solution. Then the set S
- Let A = bmatrix 2 & a & 0 1 & 3 & 1 0 & 5 & b bmatrix . If A³ = 4A² − A − 21I, where I is the identity matrix of order 3 × 3,...
- Let A = bmatrix 2 & -1 1 & 1 bmatrix . If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal to ______.
- If the system of equations x + 4y − z = λ, 7x + 9y + μz = −3, 5x + y + 2z = −1 has infinitely many solutions, then (2μ + 3λ) is...
- If the system of equations x-2y+3z=9 2x+y+z=b x-7y+az=24, has infinitely many solutions, then a – b is equal to __________.
- If the system of equations x+y+z=2 2x+4y-z=6 3x+2y+ z= has infinitely many solutions, then :
- If the system of linear equations x+y+3z=0 x+3y+k^2z=0 3x+y+3z=0 has a non-zero solution (x, y, z) for some k ∈ R, then x+ ( y z...
- The values of and for which the system of linear equations x + y + z = 2 x + 2y + 3z = 5 x + 3y + = has infinitely many solutions...
- Let = 5 and A= pmatrix & - & pmatrix . If B=A+A^4, then det(B) :
- Matrix A is such that A^2 = 2A - I where I is the identity matrix, then for n 2, A^n is equal to
- If A = bmatrix & - & bmatrix , then for n N, A^n is equal to
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