COMSATS University Islamabad, Lahore Campus
Assignment 4 SPRING 2026
Course Title:
Linear Algebra
Course Code:
MTH231 Credit Hours: 3
Course Instructor/s:
Maqsood Ahmad
Programme Name: FA25-ELC-A,B & SP25-BMD
rd
nd
Semester:
3 , 2 Batch:
Section:
A,B
Date:
15-05-2026
Time Allowed:
4
Maximum Marks:
Student’s Name:
Reg. No.
4
3
Q1: Let 𝑳: 𝑅 → 𝑅 be linear transformation for which
𝑳
𝟏
𝟎
𝟎
𝟎
Find 𝑳
𝟏
= 𝟎;𝑳
𝟏
𝟏
𝟏
𝟏
𝟏
𝟎
𝟏
𝟎
𝟎
𝟏
= 𝟎;𝑳
𝟎
𝟎
𝟎
𝟏
𝟎
𝟎
= 𝟏;𝑳
𝟏
𝟎
𝟎
𝟎
𝟏
𝟎
= 𝟏
𝟎
=?
Q2: Let 𝑳: 𝑹𝟒 → 𝑹𝟒 be linear transformation defined by
𝑳
Show 𝐷𝑖𝑚 𝐾𝑒𝑟 𝑳
𝟐𝒖𝟑 − 𝒖𝟐
𝟐𝒖𝟒 − 𝟐𝒖𝟏
=
𝒖𝟏 + 𝒖𝟒
𝒖𝟐 − 𝟐𝒖𝟑
𝒖𝟏
𝒖𝟐
𝒖𝟑
𝒖𝟒
+ 𝐷𝑖𝑚 𝑅𝑎𝑛𝑔𝑒 𝑳
= 𝐷𝑖𝑚 𝑹𝟒 .
Q3: Let 𝑳: 𝑹𝟑 → 𝑹𝟐 be linear transformation defined by
𝑳
𝒖𝟏
𝒖𝟐
𝒖𝟑
=
𝒖𝟏 + 𝒖𝟐 + 𝒖𝟑
𝒖𝟏 + 𝟐𝒖𝟐 + 𝟑𝒖𝟑
Let 𝑺 and 𝑻 be ordered basis for : 𝑹𝟑 and 𝑹𝟐, respectively. where
1 0 0
1 1
𝑆 = 1 , 1 , 0 and 𝑇 =
,
2 3
0 0 1
Find the representation (Matrix) of 𝑳 with respect to 𝑺 and 𝑻.