Q. 4 B4.3( 61 Votes )

# Construct a 2 × 2 matrix, A = [a_{ij}], whose elements are given by:

Answer :

In general, a 2 × 2 matrix is given by A =

a_{ij} =

Therefore,

a_{11} =

a_{12} =

a_{21} =

a_{22} =

Therefore, the required matrix is A = .

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If then the value of x + y is

Mathematics - ExemplarSolve for x and y:

Mathematics - Exemplar

Which of the following statements are True or False

If A and B are two square matrices of the same order, then AB = BA.

Mathematics - ExemplarIf AB = BA for any two square matrices, prove by mathematical induction that (AB)^{n} = A^{n} B^{n}.

If and , then verify (BA)^{2} ≠ B^{2}A^{2}.

Total number of possible matrices of order 3 × 3 with each entry 2 or 0 is

Mathematics - ExemplarThe matrix is a

Mathematics - ExemplarShow by an example that for A ≠ O, B ≠ O, AB = O.

Mathematics - ExemplarIf , and , verify:

(i) (AB) C = A (BC)

(ii) A(B + C) = AB + AC

Mathematics - ExemplarIf matrix , where a_{ij} = 1 if i ≠ j

a_{ij} = 0 if i = j, then A^{2} is equal to