Mat1503 Assignment 3 Determinants and Vectors

MAT1503 ASSIGNMENT 3 STUDENT NUMBER: 12596388



MAT1503 Assignment 3 Linear Algebra 1


University of South Africa


Student Number: 12596388




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, MAT1503 ASSIGNMENT 3 STUDENT NUMBER: 12596388




Question 1: MAT1503 Assignment 1


Given
𝑥 𝑦 1
Determinant =|. |=0 of matrix 𝑎1 𝑏1 1 such that a line passes
𝑎2 𝑏2 1
through the points (a1, b1) and (a2,b2)


The equation of this line can be determined as follows:


Let det (.)=x (b1-b2)-y (a1-a2) +1(a1b2-b1a2) =0
x. (b1-b2)-y. (a1-a2) =-(a1b2-b1a2)
-y (a1-a2) =-a1b2+b1a2-x (b1-b2)
−𝑎1𝑏2+𝑏1𝑎2−𝑥(𝑏1−𝑏2)
-y= where a1≠a2
𝑎1−𝑎2

Therefore the equation of the line passing through the distinct points (a1,
b1) and (a2, b2):


𝑥(𝑏1−𝑏2)+𝑎1𝑏2−𝑏1𝑎2
y= where a1≠a2
𝑎1−𝑎2




Question 2: MAT1503 Assignment 3


According to the law of transpose of matrices with respect to the
determinant function of a n*n matrix;
Det (-A) = -3. (-12-0) – (-1). (20-6)+2(0-(-3)


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