Matrices

JEE Main 2024 (Online) 4th April Evening ShiftNumericalEasy📈 Topic in 7% papers+4

Ques. 1JEE Main 2024, 4 April (Evening Shift)

Let A be a 2 2 symmetric matrix such that A bmatrix1\\1 bmatrix = bmatrix3\\7 bmatrix and the determinant of A be 1. If A-1 = A + I, where I is an identity matrix of order 2 2, then + equals .

Answer

Solution

Let A = bmatrixa & b\ & d bmatrix (symmetric), so a + b = 3 and b + d = 7.

|A| = 1 (3 - b)(7 - b) - b2 = 1 21 - 10b = 1 b = 2, hence a = 1, d = 5

A = bmatrix1 & 2\\2 & 5 bmatrix and A-1 = adj A|A| = bmatrix5 & -2\\-2 & 1 bmatrix

Also A + I = bmatrix + & 2 \\2 & 5 + bmatrix; comparing it with A-1 entry by entry:

2 = -2 = -1, and + = 5 = 6 (check: 5 + = 1)

+ = 5

Answer: 5

Keep practising — Matrices

Ques. 2JEE Main 2024, 1 February (Evening Shift)

Let A=I2-2MMT, where M is a real matrix of order 2 1 such that the relation MTM=I1 holds. If is a real number such that the relation AX= X holds for some non-zero real matrix X of order 2 1, then the sum of squares of all possible values of is equal to .

Ques. 3JEE 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

Ques. 4JEE 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. 5JEE 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 .

All Matrices PYQs →

PDFDownload Matrices PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)