MA1522 Linear Algebra for Computing Assignment 1 AY 2026/27 Semester 1 NUS

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Published: 28 Jul, 2026
Category Assignment Subject Mathematics
University National University Of Singapore Module Title MA1522 Linear Algebra

MA1522 Linear Algebra for Computing

Homework Assignment 1

Deadline: 9 Feb 2024 23:59

1. Consider the following linear system

  • 4x1+2x2+4x3=0
  • 5x1+4x2=1
  • 4x1+x2+2x3=5.

(i) In every row-echelon form of the augmented matrix corresponding to the given linearsystem, how many pivot columns are there?

(ii) How many arbitrary parameters are needed to describe a general solution for the givenlinear system?

(iii) How many solutions are there for the given linear system?

(iv) Find the solution of the linear system.

2. Consider the following linear system:

  • ax +y+z=a3
  • x+a y +z=1
  • x+y+az =a,

where ais a real constant. Find the conditions on asuch that

(i) the system has no solution;
(ii) the system has a unique solution;
(iii) the system has infinitely many solutions.

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