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ESE Achiever's plan || Paper 1 || Linear Algebra

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Question 1

If A is 3 × 3 matrix and trace A = 9, |A| = 24 and one of the eigen values is 3, then sum of other eigen values is_____.

Question 2

The system of equation kx + 2y – z = 1, (k – 1) y – 2z = 2 and (k + 2)z = 3 will have unique solution if k =

Question 3

For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?

Question 4

If 2, – 4, 3 are the eigen values of some 3 × 3 matrix A, then A^–1 =

Question 5

A (3 × 2) matrix is given as

. If the eigen values of the matrix are real and positive, then which one of the following relations should be satisfied?

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Mar 7ESE & GATE EC