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*Answer can only contain numeric values

Linear Algebra NAT Level - 1 - Question 1

What is the maximum value of λ, for which the given system is inconsistent?

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

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Linear Algebra NAT Level - 1 - Question 2

Given a matrix,

What would be the sum of eigenvalues of A^{–1}? (Give the answer upto 3 decimal places )

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Linear Algebra NAT Level - 1 - Question 3

Consider the matrix Then find the product of eigenvalues?

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Linear Algebra NAT Level - 1 - Question 4

The three equations,

–2x + y + z = a

x – 2y + z = b

x + y – 2z = c

has

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Linear Algebra NAT Level - 1 - Question 5

Consider the following equations

x + y – 3z + 2w = 0

2x – y + 2z – 3w = 0

3x – 2y + z – 4w = 0

–4x – y + 3z + 4w = 0

Find the rank of the coefficient matrix.

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Linear Algebra NAT Level - 1 - Question 6

If x = y = z = αc satisfy the matrix equation AX = 0 where

then find the value of α.

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Linear Algebra NAT Level - 1 - Question 7

For which value of λ will the following equations fail to have unique solution?

3x – y + λz = 1

2x + y + z = 2

x + 2y – λz = –1

Detailed Solution for Linear Algebra NAT Level - 1 - Question 7

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Linear Algebra NAT Level - 1 - Question 8

Let A be a 3 × 3 matrix with eigen values 1, –1, 0. Then the determinant of I + A^{100} is :

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Linear Algebra NAT Level - 1 - Question 9

The system of equations αx + y + z = α - 1, x + αy + z = α - 1, x + y + αz = α - 1 has no solution. Find the maximum value of α

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