1:
A set of orthogonal vectors -
1) are linearly independent
2) can be converted to orthonormal vectors by dividing them by their
respective length
3) adhere to trace(transpose(A).B) = 0
4) are linearly independent and the corollary is ALSO true
Which of the above statements is TRUE -

Options:

- 1,2,3
- 1,3,4
- 1,3
- 2,4

Answer: Option 1

Explanation:

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2:
Rank -

Options:

- of a null matrix doesn't exists
- of any matrix other than null matrix is > or = 1
- of any matrix other than null matrix is > or = 2
- of any matrix other than null matrix is > or = 0

Answer: Option 2

Explanation:

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3:
Rank of a matrix -

Options:

- can be calculated ONLY if the matrix is square
- is the order of largest square sub-matrix present in a matrix
- is the same as no. of linearly dependent row or coloumn vectors in the matrix
- is the order of largest non-singular square sub-matrix present in a matrix

Answer: Option 4

Explanation:

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4:
Let A be a square matrix, then, the solution of characteristic equation
|A-kI|=0 is equal to -

Options:

- Product of Eigen values of A
- Eigen values of A-kI
- Product of Eigen values of A-kI
- None of the above

Answer: Option 1

Explanation:

1) |A| is itself a solution of this characteristic equation which otherwise gives eigen values of A 2) Product of eigen values of A = |A| Discuss this in Forums

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5:
In an under-determined (means No. of equations < No. of variables) system of Linear non-homogeneous eq's -

Options:

- We can have only consistent and infinite solution
- We can have either inconsistent or consistent and infinite solution
- We can have a consistent and unique solution
- We can have every possible solution

Answer: Option 2

Explanation:

In an under-determined system,either - 1) Rank(A) is not equal to Rank(A|B) OR 2) If Rank(A) is equal to Rank(A|B), Rank(A) will always be less than n So, we will ONLY get infinite no. of solutions. Discuss this in Forums

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6:
The sum of all the diagonal elements of a matrix A -

Options:

- Is equal to the product of eigen values
- is always less than |A|
- is always greater than |A|
- is equal to the trace of A

Answer: Option 4

Explanation:

By definition, Trace of a square matrix = Sum of its diagonal elements = Sum of all its eigen values Discuss this in Forums

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7:
If a row or coloumn of a matrix A undergoes transformation given by Ri+kRj or Ci+kCj respectively, the value of determinant of new matrix is-

Options:

- k times |A|
- zero
- remains equal to |A|
- changes to a new value not related to |A|

Answer: Option 3

Explanation:

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8:
Let A,B,C,D,E be n*n matrices, each with non-zero determinant and ABCDE = I, where I = Identity matrix of order n,
Then C =

Options:

- (B^-1)*(A^-1)*(E^-1)*(D*-1)
- (A^-1)*(B^-1)*(D^-1)*(E*-1)
- (ABDE)^-1
- (EDBA)*-1

Answer: Option 1

Explanation:

ABCDE = I BCDE = (A^-1) Pre-Multiplying with A^-1 on both sides CDE = (B^-1)*(A^-1) Pre-Multiplying with B^-1 on both sides CD = (B^-1)*(A^-1)*(E^-1) Post-Multiplying with E^-1 on both sides C = (B^-1)*(A^-1)*(E^-1)*(D^-1) Post-Multiplying with D^-1 on both sides Discuss this in Forums

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9:
A = a1 a2 a3
b1 b2 b3
c1 c2 c3
Then, a1*cof(b1) + a2*cof(b2) + a3*cof(b3) =

Options:

- |A|
- Has no meaning
- Zero
- None of the above

Answer: Option 3

Explanation:

The sum of the products of the elements of any row (or coloumn) with cofactors of some other row (or coloumn) respectively is ALWAYS zero. Discuss this in Forums

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10:
Let A = 1 1 3
5 2 6
-2 -1 -3
It is seen that A^3 = 0. So, A is a-

Options:

- Singular Matrix
- Nilpotent Matrix of order 3
- Null Matrix
- None of the above

Answer: Option 2

Explanation:

If for any matrix A, A^n = 0, then A is called a Nilpotent Matrix of order n Discuss this in Forums

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