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Linear Algebra NAT Level - 2 - Question 1

If (a, 6) are the values for which the given equations are inconsistent.

x + 2y + 3z = 4

x + 3y + 4z = 5

x + 3y + az = b

then the value of a is :

Detailed Solution for Linear Algebra NAT Level - 2 - Question 1

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Linear Algebra NAT Level - 2 - Question 2

If z = 7c, then find the value of x such that the given equations has infinite solution

x + 3y – 2z = 0

2x – y + 4z = 0

x – 11y + 14z = 0

Detailed Solution for Linear Algebra NAT Level - 2 - Question 2

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*Answer can only contain numeric values

Linear Algebra NAT Level - 2 - Question 3

A matrix M has eigenvalues 1 and 4 with corresponding eigenvectors (1, –1)^{T} and (2, 1)^{T} respectively. Then M is given by Find the value of α

Detailed Solution for Linear Algebra NAT Level - 2 - Question 3

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Linear Algebra NAT Level - 2 - Question 4

The only real value of λ for which the following equations have non-zero solution is,

x + 3y + 3z = λx

3x + y + 2z = λy

2x + 3y + z = λz

Detailed Solution for Linear Algebra NAT Level - 2 - Question 4

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Linear Algebra NAT Level - 2 - Question 5

For what value of c the following given equations will have infinite number of solutions?

–2x + y + z = 1

x – 2y + z = 1

x + y – 2z = c

Detailed Solution for Linear Algebra NAT Level - 2 - Question 5

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Linear Algebra NAT Level - 2 - Question 6

Find the rank of the matrix for the following equations :

3x + 4y – z – 6w = 0

2x + 3y + 2z – 3w = 0

2x + y – 14z – 9w = 0

x + 3y + 13z + 3w = 0

Detailed Solution for Linear Algebra NAT Level - 2 - Question 6

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Linear Algebra NAT Level - 2 - Question 7

Let A be a 3 × 3 matrix. Suppose that the eigenvalues of A are –1, 0, 1 with respective eigenvectors (1,–1,0)^{T}, (1,1,–2)^{T} & (1,1,1)^{T}. Then 6A is given by Find the value of α

Detailed Solution for Linear Algebra NAT Level - 2 - Question 7

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Linear Algebra NAT Level - 2 - Question 8

Find the rank of the matrix for the following equations :

4x + 2y + z + 3u = 0

6x + 3y + 4z + 7u = 0

2x + y + u = 0

Detailed Solution for Linear Algebra NAT Level - 2 - Question 8

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Linear Algebra NAT Level - 2 - Question 9

Solution of the system,

3x – 2y – w = 2

2y + 2z + w = 1

x – 2y – 3z + 2w = 3

y + 2z + w = 1

is given by (1, 0, 0, α)^{T}. Find the value of α.

Detailed Solution for Linear Algebra NAT Level - 2 - Question 9

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Linear Algebra NAT Level - 2 - Question 10

Let a real symmetric matrix. P is the orthogonal matrix such that P^{-1} AP is a diagonal matrix given by Find the value of α

Detailed Solution for Linear Algebra NAT Level - 2 - Question 10

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