Q. 63.7( 27 Votes )

# Find the values of x, y, z if the matrix satisfy the equation A’A =I.

Answer :

Given A

*Transpose of a matrix: If A be an m×n matrix, then the matrix obtained by interchanging the rows and columns of A is called the transpose of A. It is denoted by A’ or A ^{T}.*

∴ Transpose of A = A’ =

Given equation

A’A =I

=

=

. =

As these matrices are equal to each other that means each element of matrix on L.H.S is equal each element of matrix on R.H.S.

∴ On comparing elements on both sides we get

4y^{2} + z^{2} = 1 …… (1)

2y^{2} – z^{2} = 0 …… (2)

x^{2} + y^{2} + z^{2} = 1 …… (3)

– y^{2} – z^{2} = 0 …… (4)

From equation (4) we get,

x^{2} = y^{2} + z^{2} …… (5)

Substituting this value in equation (3) we get,

2y^{2} + 2z^{2} = 1 …… (6)

Subtracting equation (2) and (6) we get,

3z^{2} = 1

z^{2} = 1/3

**z =** **1/3**

Substituting value of z in equation (2) we get,

2y^{2} = 1/3

y^{2} = 1/6

**y = �1/6**

Substituting values of y and z in equation (5) we get,

x^{2} = 1/2

**x = 1/2**

Hence values of x, y, z are 1/2, 1/6, 1/3 respectively.

Rate this question :

Which of the following statements are True or False

Transpose of a column matrix is a column matrix.

Mathematics - ExemplarWhich of the following statements are True or False

Transpose of a column matrix is a column matrix.

Mathematics - ExemplarGiven and . Is (AB)’ = B’A’?

Mathematics - ExemplarWhich of the following statements are True or False

If A and B are any two matrices of the same order, then (AB)’ = A’B’.

Mathematics - ExemplarWhich of the following statements are True or False

If then AB and BA are defined and equal.

Mathematics - ExemplarFor the following matrices A and B, verify that (AB)’ = B’A’.

Mathematics - Board Papers

Which of the following statements are True or False

If A and B are any two matrices of the same order, then (AB)’ = A’B’.

Mathematics - ExemplarUse the product to solve the system of equations

Mathematics - Board Papers