8/7/2019 EndsemLA_Qpaper

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Indian Institute of Technology Guwahati

End-semester Examination

MA 101 (Mathematics - I)

Part I (Linear Algebra) : Maximum Marks : 10

Date : November 23, 2010 Time : 1 pm - 4 pm (including Part II)

1. Let B be an n× n matrix with distinct eigenvalues. Show that every n× n matrix A such

that AB = BA is diagonalizable. [4]

2. Prove or disprove: If A =

5 4 14 04 13 14 0

14 14 49 00 0 0 −1

,

then there exists a symmetric matrix B such that A = B52. [4]

3. Find an orthonormal basis for the column space of 

1 1 1 11 1 1 11 1 1 11 1 1 2

. [2]

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