Test: Matrices- 1 - JEE MCQ

# Test: Matrices- 1 - JEE MCQ

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## 25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Matrices- 1

Test: Matrices- 1 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Matrices- 1 questions and answers have been prepared according to the JEE exam syllabus.The Test: Matrices- 1 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Matrices- 1 below.
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Test: Matrices- 1 - Question 1

### The number of all possible matrices of order 3×3 with each entry 0 if 1 is

Detailed Solution for Test: Matrices- 1 - Question 1

23x3 = 29 = 512.

The number of elements in a 3 X 3 matrix is the product 3 X 3=9.

Each element can either be a 0 or a 1.

Given this, the total possible matrices that can be selected is 29=512

Test: Matrices- 1 - Question 2
Detailed Solution for Test: Matrices- 1 - Question 2

If any row or column of a square matrix is 0 , then its product with itself is always a zero matrix.

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Test: Matrices- 1 - Question 3

### This matrix is a _______ .

Test: Matrices- 1 - Question 4

Two matrices A and B are multiplicative inverse of each other only if

Detailed Solution for Test: Matrices- 1 - Question 4

If AB = BA = I , then A and B are inverse of each other. i.e. A is invers of B and B is inverse of A.

Test: Matrices- 1 - Question 5

For what value of λ the following system of equations does not have a solution ? x + y + z = 6, 4x + λy - λz = 0, 3 x + 2y – 4 z = - 5

Detailed Solution for Test: Matrices- 1 - Question 5

The given system of equations does not have solution if :

⇒ (24 + 6λ - 14λ) = 0 ⇒ λ = 3

Test: Matrices- 1 - Question 6

I2 is the matrix

Detailed Solution for Test: Matrices- 1 - Question 6

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context

Test: Matrices- 1 - Question 7

Let A be any m×n matrix, then A2 can be found only when

Detailed Solution for Test: Matrices- 1 - Question 7

The product of any matrix with itself can be found only when it is a square matrix.i.e. m = n.

Test: Matrices- 1 - Question 8

The order of the single matrix obtained from is

Detailed Solution for Test: Matrices- 1 - Question 8

Test: Matrices- 1 - Question 9

If A and B are square matrices of the same order, then(A+B)2 = A2+2AB+B2 implies

Detailed Solution for Test: Matrices- 1 - Question 9

If A and B are square matrices of same order , then , product of the matrices is not commutative.Therefore , the given result is true only when AB = BA.

Test: Matrices- 1 - Question 10

The value of λ, for which system of equations. x + y + z = 1, x + 2y + 2z = 3, x + 2y + λz = 4, have no solution is

Detailed Solution for Test: Matrices- 1 - Question 10

The given system is:

Therefore, the correct answer is: λ=2.

Test: Matrices- 1 - Question 11

If A is a matrix of order 3 × 4 , then each row of A has

Detailed Solution for Test: Matrices- 1 - Question 11

, therefore matrix A has 4 elements in each row

Test: Matrices- 1 - Question 12

If A and B are any two matrices, then

Detailed Solution for Test: Matrices- 1 - Question 12

Let matrix A is of order m x n , and matrix B is of order p x q . then , the product AB is defined only when n = p. that’s why, If A and B are any two matrices, then AB may or may not be defined.

Test: Matrices- 1 - Question 13

If, we are given a square matrix A then, Adj.(KA) = ….

Detailed Solution for Test: Matrices- 1 - Question 13

Adj.(KA) = Kn−1 Adj.A , where K is a scalar and A is a n x n matrix.

Test: Matrices- 1 - Question 14

Detailed Solution for Test: Matrices- 1 - Question 14

Test: Matrices- 1 - Question 15

The system of equations,x + y = 2 and 2x + 2y = 3 has

Detailed Solution for Test: Matrices- 1 - Question 15

For No solutions,   for given system of equations we have

Test: Matrices- 1 - Question 16

If P is of order 2 × 3 and Q is of order 3 × 2, then PQ is of order

Detailed Solution for Test: Matrices- 1 - Question 16

Here, matrix P is of order 2 × 3 and matrix Q is of order 2 × 2 , then , the product PQ is defined only when : no. of columns in P = no. of rows in Q. And the order of resulting matrix is given by : rows in P x columns in Q.

Test: Matrices- 1 - Question 17

A square matrix A = [aij]n×n is called a lower triangular matrix if aij = 0 for

Detailed Solution for Test: Matrices- 1 - Question 17

Lower triangular matrix is given by :
,

here , aij = 0
if i is less than j.and aij ≠ 0, if i is greater than j.

Test: Matrices- 1 - Question 18

If A and B are any two square matrices of the same order, then

Detailed Solution for Test: Matrices- 1 - Question 18

By the property of transpose , (AB)’ = B’A’.

Test: Matrices- 1 - Question 19

The transformation ‘orthogonal projection on X-axis’ is given by the matrix

Detailed Solution for Test: Matrices- 1 - Question 19

The orthogonal projection on x- axis is given by :

Test: Matrices- 1 - Question 20

The equations x + 2y + 2z = 1 and 2x + 4 y + 4z = 9 have

Detailed Solution for Test: Matrices- 1 - Question 20

Test: Matrices- 1 - Question 21

The number of all the possible matrices of order 2 × 2 with each entry 0, 1 or 2 is

Detailed Solution for Test: Matrices- 1 - Question 21

32x2 = 34 = 81

Test: Matrices- 1 - Question 22

A square matrix  A = [aij]n×n is called an upper triangular if aij = 0 for

Detailed Solution for Test: Matrices- 1 - Question 22

Upper Triangular matrix is given by  :
.
Here, aij=0 , if i is greater than j.and aij ≠ 0, if I is less than j.

Test: Matrices- 1 - Question 23

If A is any square matrix, then

Detailed Solution for Test: Matrices- 1 - Question 23

For every square matrix (A + A’) is always symmetric.

Test: Matrices- 1 - Question 24

The equations, x + 4 y – 2 z = 3, 3 x + y + 5 z = 7, 2 x + 3y +z = 5 have

Detailed Solution for Test: Matrices- 1 - Question 24

The given system of equations does not have solution if :

- 0 ⇒ 1(-14) - 4(-7) -2(7) = 0

Test: Matrices- 1 - Question 25

If the system of equationsx + 4 ay + az = 0, x + 3by + bz = 0 andx + 2 cy +cz = 0 have a non-zero solution,then a, b, c are in

Detailed Solution for Test: Matrices- 1 - Question 25

For a non trivial solution :

⇒ bc + ab - 2ac = 0 ⇒  ∴ there, a , b ,c, are in H.P

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests