JEE Main Matrices and Determinants Practice Questions With Solutions

Updated By Diksha Sharma on 07 Jan, 2025 21:16

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JEE Main Mathematics Matrices and Determinants Practice Questions

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Question 1.

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Let B=[1315] and A be a 2×2 matrix such that AB1=A1. If BCB1=A and C4+αC2+βI=O, then 2βα is equal to

Question 2.

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Let λ,μR. If the system of equations

3x+5y+λz=37x+11y9z=297x+155y189z=μ

has infinitely many solutions, then μ+2λ is equal to :

Question 3.

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If αa,βb,γc and |αbcaβcabγ|=0, then aαa+bβb+γγc is equal to :

Question 4.

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If the system of equations x+4yz=λ,7x+9y+μz=3,5x+y+2z=1 has infinitely many solutions, then (2μ+3λ) is equal to :

Question 5.

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Let A=[2a013105b]. If A3=4A2A21I, where I is the identity matrix of order 3×3, then 2a+3b is equal to

Question 6.

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If A is a square matrix of order 3 such that det(A)=3 and det(adj(4adj(3adj(3adj((2A)1)))))=2m3n, then m+2n is equal to :

Question 7.

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For α,βR and a natural number n, let Ar=|r1n22+α2r2n2β3r23n(3n1)2|. Then 2A10A8 is

Question 8.

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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 solutions, satisfy the equation :

Question 9.

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Let αβ0 and A=[βα3ααββα2α]. If B=[3α93αα72α2α52β] is the matrix of cofactors of the elements of A, then det(AB) is equal to :

Question 10.

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Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2. Then |ATA(adj(2A))1(adj(4B))(adj(AB))1AAT| is equal to :

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Question 1.

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If the system of equations

11x+y+λz=52x+3y+5z=38x19y39z=μ

has infinitely many solutions, then λ4μ is equal to :

Question 2.

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Let A=[1201] and B=I+adj(A)+(adjA)2++(adjA)10.Then, the sum of all the elements of the matrix B is:

Question 3.

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Let α(0,) and A=[12α101012]. If det(adj(2AAT)adj(A2AT))=28, then (det(A))2 is equal to:

Question 4.

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If the system of equations

x+(2sinα)y+(2cosα)z=0x+(cosα)y+(sinα)z=0x+(sinα)y(cosα)z=0

has a non-trivial solution, then α(0,π2) is equal to :

Question 5.

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Let the system of equations x+2y+3z=5,2x+3y+z=9,4x+3y+λz=μ have infinite number of solutions. Then λ+2μ is equal to :

Question 6.

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If A=[2112],B=[1011],C=ABAT and X=ATC2A, then detX is equal to :

Question 7.

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If the system of equations

2x+3yz=5x+αy+3z=43xy+βz=7

has infinitely many solutions, then 13αβ is equal to :

Question 8.

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Let A be a 3×3 real matrix such that

A(101)=2(101),A(101)=4(101),A(010)=2(010)

Then, the system (A3I)(xyz)=(123) has :

Question 9.

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If the system of linear equations

x2y+z=42x+αy+3z=53xy+βz=3

has infinitely many solutions, then 12α+13β is equal to

Question 10.

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Let R=(x000y000z) be a non-zero 3×3 matrix, where xsinθ=ysin(θ+2π3)=zsin(θ+4π3)0,θ(0,2π). For a square matrix M, let trace (M) denote the sum of all the diagonal entries of M. Then, among the statements:

(I) Trace (R)=0

(II) If trace (adj(adj(R))=0, then R has exactly one non-zero entry.

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