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Linear Algebra MCQ Level - 1 - Question 1

Let A be a m × n matrix with row rank = r = column rank. The dimension of the space of solution of the system of linear equations AX = 0 is :

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

Linear Algebra MCQ Level - 1 - Question 2

What would be the dimension for the general solution of the homogeneous system.

*x*_{1} + 2*x*_{2} – 3*x*_{3} + 2*x*_{4} – 4*x*_{5} = 0

2*x*_{1} + 4*x*_{2} – 5*x*_{3} + *x*_{4} – *6*x* _{5}* = 0

5

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

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Detailed Solution for Linear Algebra MCQ Level - 1 - Question 3

Linear Algebra MCQ Level - 1 - Question 4

A matrix M has eigen values 1 and 4 with corresponding eigen vectors (1, –1)^{T} and (2, 1)^{T}, respectively. Then M is :

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Linear Algebra MCQ Level - 1 - Question 5

If rank of matrix A is 5 and nullity of A is 3, then A is of order :

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Linear Algebra MCQ Level - 1 - Question 6

The three equations,

–2x + y + z = a

x – 2y + z = b

x + y – 2z = c

will have no solution, unless :

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Linear Algebra MCQ Level - 1 - Question 8

The matrix A is represented as . The transpose of the matrix of this matrix is represented as?

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Linear Algebra MCQ Level - 1 - Question 9

Find the values of x, y, z and w from the below condition.

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Linear Algebra MCQ Level - 1 - Question 10

Let P be a matrix of order m × n and Q be a matrix of order n × p, n ≠ p. If rank (P) = n and rank of (Q) = p, then rank (PQ) is :

Detailed Solution for Linear Algebra MCQ Level - 1 - Question 10

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