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MAT1503
Assignment 3
(692080)
DUE: 26 June 2023 at 2:00PM
UnisaGuides
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,Given,
If the determinant of the matrix is zero,
it implies that the three rows of the matrix are linearly dependent, meaning that one row
can be expressed as a linear combination of the other two rows
In terms of points, this means that the three points (a, b), (c, d), and (e, f) lie on the same
line.
Expand the determinant of the matrix using the first row:
Simplifying the expression
Rearrange the terms to group the variables
The equationa(d−f)+b(e−c)+c(f−d)=0 implies that the three terms are equal to zero, which
means that the three expressions (d−f),(e−c),and(f−d)are all zero
Since each of these expressions evaluates to zero, it implies that d=f,e=c,andf=d This
shows that the points (a,b),(c,d),and(e,f) lie on the same line, making them collinear.
hence, we have proved that points (a, b), (c, d), and (e, f) are collinear whenever the
determinant of the matrix is equal to zero.
Explanation:
we used the concept of linear dependence
, slope=b₂−b₁/a₂−a₁
Then, using the point-slope form of the equation of a line, we have:
y−b₁=slope×(x−a₁)
y=slope×(x−a₁)+b₁
Substituting the value of the slope, the equation becomes
y=(b₂−b₁/a₂−a₁)×(x−a₁)+b₁
This is the equation of the line passing through the distinct points (a₁, b₁) and (a₂, b₂)
Explanation:
Using the slope formula we find the slope and then putting all value in the equation
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