Test: Linear Algebra - 4


20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Test: Linear Algebra - 4


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QUESTION: 1

For a positive integer n, let denote the vector space of polynomials in one variable x with real coefficients and with degree < n. Consider the map defined by T (p (x)) = p (x2), then

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QUESTION: 2

Let A be a real 3 x 4 matrix of rank 2, then the rank of At A, where At deonles the transpose of A. is

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QUESTION: 3

Let V be the space of twice differentiable functions satisfying f" - 2f' + f = 0. Define by T(f') = (f'(0), f(0)), then T is

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QUESTION: 4

The determinant 

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QUESTION: 5

Which of Ihe following matrices has the same row space as the matrix 

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QUESTION: 6

The determinant of the n x n permutation 

[x] denotes greatest integer function of x.

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QUESTION: 7

The row space of a 20 x 50 matrix A has dimention 13. What is the dimension of the space of solution of Ax = 0?

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QUESTION: 8

Given a permutation the matrix A is defined to be the one whose ith column is the σ(i)th column of the Identity matrix I. Which of the following is correct?

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QUESTION: 9

For the matrix A as given below, which of them satisfy A6 = I?

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QUESTION: 10

Let I denote the 4 x 4 Identity matrix. If the roots of the characteristic polynomial of a 4 x 4 matrix M 

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QUESTION: 11

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QUESTION: 12

Let M be the set of all invertibel 5 x 5 matrices with entries 0 and 1. For each m ∈ M, let n1 (m) and n0(m) denote the number of 1's and 0's in m respectively then

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QUESTION: 13

 and b a non zero vector such that Mx = b for some Then the value of xTb is 

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QUESTION: 14

The matrix  is a unitary matrix when α is 

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QUESTION: 15

Let P be the vector space over all polynomials of degree less than 3 with real coefficients. Consider the linear transformation T : P → P defined by
T(a0 + a1x + a2x2 + a3x3) = a3 + a2x + a1x2 + a0x3

Then the matrix representation of M of T with respect to the ordered basis {1, x, x2,x3} satisfies 

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QUESTION: 16

The largest eigenvalue of the matrix 

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QUESTION: 17

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QUESTION: 18

Let a,b,c,d be distinct non zero real numbers with a + b = c + d. Then an eigenvalue of the matrix 

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QUESTION: 19

The system of linear equations 
x - y + 2z = b1 
x + 2y - z = b2
2y - 2z = b3
is inconsistent when (b1, b2, b3) equals

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*Multiple options can be correct
QUESTION: 20

Let X and Y are n x n matrices with real entries, then which of the following is(are) true?

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