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FOURTH SEMESTER (CBCSS-UG) DEGREE EXAMINATION, APRIL 2022

Time :

Mathematics
MTS 4B 04—LINEAR ALGEBRA
(2019 Admission onwards)
Two Hours and a Half Maximum : 80 Marks
Section A (Short Answer Type Questions)

Answer at least ten questions.

Each question carries 3 marks.

All questions can be attended.
Overall Ceiling 30.

Show that the linear system of equations 4x—2y=1 has infinitely many solutions.
16x-8y =4
Write any two facts about row echelon forms and reduced row echelon forms.

Express the linear system 42] - 328 + 4 = 1
5] + ॐ - 84 = 3

220 - 5 + 9.8 - 4 = 0

92௦௦-0 4701-2

in the form AX = B.
Let V = R? and define addition and scalar multiplication as follows. For ६ (७1,५४३ ),)० 5 (०1,०५० ),

‎for a real number k, ku =(kuw,,0). For w=(1,1) and v0 =(-3,5) find‏ 4قصد ( وہ + ولا + يله) < تاج عا
‎ठ 804 0 k=5,find zz . Also show that one axiom for vector space is not satisfied.‏ + ्

‎Define basis for a vector space.

‎How will you relate the dimension of a finite dimensional vector space to the dimension of its
subspace. Give two facts.

‎Give a solution to the change of basis problem.

‎When you can say that a system of linear equation Ax = b is consistent. What is meant by a
particular solution of the consistent system Ax =b.

‎Find the rank of a 5 x 7 matrix A for which Ax = 0 has a two-dimensional solution space.

‎Turn over

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