Maths-

General

Easy

Question

# If k is an orthogonal matrix then k is equal to-

- 1
- 1/2
- 1/3
- None of these

## The correct answer is: 1/3

### Let A = k A^{T} = k

Since A is orthogonalAA^{T} = I

k^{2} = I

k^{2}= I 9k^{2} I = I k^{2} = 1/9 k = ±1/3

### Related Questions to study

maths-

### If A = , B = and X is a matrix such that A = BX, then X equals-

### If A = , B = and X is a matrix such that A = BX, then X equals-

maths-General

maths-

### If A is a square matrix such that A^{2} = A, then |A| equals-

### If A is a square matrix such that A^{2} = A, then |A| equals-

maths-General

maths-

### The value(s) of m does the system of equations 3x + my = m and 2x – 5y = 20 has a solution satisfying the conditions x > 0, y > 0

### The value(s) of m does the system of equations 3x + my = m and 2x – 5y = 20 has a solution satisfying the conditions x > 0, y > 0

maths-General

maths-

### If A^{k} = 0, for some value of k, (I – A)^{p} = I + A + A^{2} + …. A^{k–1}, thus p is (A is nilpotent with index k).

### If A^{k} = 0, for some value of k, (I – A)^{p} = I + A + A^{2} + …. A^{k–1}, thus p is (A is nilpotent with index k).

maths-General

maths-

### If the matrix A = has rank 3, then -

### If the matrix A = has rank 3, then -

maths-General

maths-

### If A is non-singular matrix of order 3 × 3, then adj (adj A) is equal to -

### If A is non-singular matrix of order 3 × 3, then adj (adj A) is equal to -

maths-General

maths-

### For k =, the value of a, b, c such that PP' = I, where P = is-

### For k =, the value of a, b, c such that PP' = I, where P = is-

maths-General

maths-

### If matrix A = where a, b, c are real positive numbers, abc = 1 and A^{T} A = 1, then the value of a^{3} + b^{3} + c^{3} is -

### If matrix A = where a, b, c are real positive numbers, abc = 1 and A^{T} A = 1, then the value of a^{3} + b^{3} + c^{3} is -

maths-General

maths-

### If [x] stands for the greatest integer less or equal to x, then in order than the set of equations x – 3y = 4 ; 5x + y = 2 ; [2]x – [e]y = [2a] may be consistent, then ‘a’ should lie in -

### If [x] stands for the greatest integer less or equal to x, then in order than the set of equations x – 3y = 4 ; 5x + y = 2 ; [2]x – [e]y = [2a] may be consistent, then ‘a’ should lie in -

maths-General

maths-

### If the matrix is orthogonal, then -

### If the matrix is orthogonal, then -

maths-General

maths-

### For each real x such that . Let A (x) denote the matrix (1 – x)^{–1/2} and where and z = then k is -

### For each real x such that . Let A (x) denote the matrix (1 – x)^{–1/2} and where and z = then k is -

maths-General

maths-

### If the system of equations x + 2y – 3z = 2, (k + 3)z = 3, (2k + 1)y + z = 2 is inconsistent, then value of k can be -

### If the system of equations x + 2y – 3z = 2, (k + 3)z = 3, (2k + 1)y + z = 2 is inconsistent, then value of k can be -

maths-General

maths-

### If A is a 3 × 3 skew-symmetric matrix, then |A| is given by -

### If A is a 3 × 3 skew-symmetric matrix, then |A| is given by -

maths-General

chemistry-

The solubility of iodine in water is greatly increased by:

The solubility of iodine in water is greatly increased by:

chemistry-General

maths-

### Let A = if A^{–1} = xA + yI_{2} then x and y are respectively -

### Let A = if A^{–1} = xA + yI_{2} then x and y are respectively -

maths-General