HARD
JEE Main
IMPORTANT
Earn 100

The set of all values of λ for which the system of linear equations:
2 x 1 - 2 x 2 + x 3 = λ x 1
2 x 1 - 3 x 2 + 2 x 3 = λ x 2
- x 1 + 2 x 2 = λ x 3
has a non-trivial solution,

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Important Questions on Matrices and Determinants

HARD
JEE Main
IMPORTANT
If A is a  3×3 matrix such that 5 adjA=5, then A is equal to
MEDIUM
JEE Main
IMPORTANT
If x2+xx+1x-22x2+3x-13x3x-3x2+2x+32x-12x-1=ax-12 , then a is equal to:
HARD
JEE Main
IMPORTANT
If Δr=r2r-13r-2n2n-1a12nn-1 n-1212n-13n+4, then the value of r=1n1Δr
EASY
JEE Main
IMPORTANT
Let A and B be any two 3 × 3  matrices. If A is symmetric and B is skew symmetric, then the matrix AB-BA is 
MEDIUM
JEE Main
IMPORTANT

If a, b, c  are non - zero real numbers and if the system of equations

a-1x=y+z

b-1y=x+z

c-1z=x+y

has a non - trivial solution, then ab+bc+ca  equals :

MEDIUM
JEE Main
IMPORTANT

If B is a 3×3  matrix such that B2=0, then det. I+B50-50B is equal to :

HARD
JEE Main
IMPORTANT
If α, β0, fn=αn+βn and 31+f11+f21+f11+f21+f31+f21+f31+f4=K1-α21-β2α-β2, then K is equal to 
HARD
JEE Main
IMPORTANT
If A is a 3×3 non-singular matrix such that AA'=A'A and B=A-1A', then BB' equals, where X' denotes the transpose of the matrix X.