Matrices

JEE Main 2024 (Online) 29th January Morning ShiftMCQEasy📈 Topic in 7% papers+4−1

Ques. 1JEE Main 2024, 29 January (Morning Shift)

Let A be a square matrix such that AAT=I. Then 12A [ (A+AT )2+ (A-AT )2 ] is equal to

A2+AT
A3+I
A3+AT
A2+I

Answer

(3) A3+AT

Solution

(A+AT )2+ (A-AT )2

= (A2+AAT+ATA+(AT)2 )+ (A2-AAT-ATA+(AT)2 )

=2A2+2(AT)2

∴ Expression = 12A [2A2+2(AT)2 ]=A3+(AAT)AT

=A3+IAT=A3+AT, as AAT=I

Answer: (3)

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Ques. 2JEE Main 2024, 27 January (Morning Shift)

Consider the matrix f(x)= bmatrix x & - x & 0\ x & x & 0\ 0 & 0 & 1 bmatrix. Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

Statement I is false but Statement II is true
Both Statement I and Statement II are false
Both Statement I and Statement II are true
Statement I is true but Statement II is false

Ques. 3JEE Main 2024, 27 January (Evening Shift)

Let A be a 2 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A-xI|=0 be -1 and 3, then the sum of the diagonal elements of the matrix A2 is .

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