Test: Matrices- 1 - JEE MCQ

2^3x3 = 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

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

The matrix given in the image is a diagonal matrix.

• A diagonal matrix is one in which all the elements outside the main diagonal are zero, and the elements on the main diagonal can be any value.
• Here, the non-zero entries (6, 3, 9) are all on the main diagonal, and all other elements are zero.

Correct answer: c) diagonal matrix.

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.

The given system of equations does not have solution if :

⇒ (24 + 6λ - 14λ) = 0 ⇒ λ = 3

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 I_n, or simply by I if the size is immaterial or can be trivially determined by the context

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

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.

The given system is:

Therefore, the correct answer is: λ=2.

, therefore matrix A has 4 elements in each row

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.

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

For No solutions,   for given system of equations we have 

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.

Lower triangular matrix is given by : 
 ,

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

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

The orthogonal projection on x- axis is given by : 

3^2x2 = 3⁴ = 81

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

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

The given system of equations does not have solution if : 

- 0 ⇒ 1(-14) - 4(-7) -2(7) = 0

For a non trivial solution : 

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