SOLUTION: steps and solution how to solve this question: M is the matrix (3 4) (p q) If M is a singular matrix and p=2,calculate the value of q.

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Question 940542: steps and solution how to solve this question:
M is the matrix (3 4)
(p q)
If M is a singular matrix and p=2,calculate the value of q.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
M is the matrix
M=%28matrix%282%2C2%2C3%2C4%2Cp%2Cq%29%29

If M is a singular matrix and p=2,calculate the value of q:
A square matrix which does not have an inverse. A matrix is singular if and only if its determinant is zero.
so, D=3q-4p=0
substitute p=2
3q-4%2A2=0
3q-8=0
3q=8
q=8%2F3
check:
Solved by pluggable solver: Finding the Determinant of a 2x2 Matrix

If you have the general 2x2 matrix:

%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29

the determinant is: D=a%2Ad-c%2Ab

So this means that

abs%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29=a%2Ad-c%2Ab

Note: the vertical bars denote a determinant.


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So in this case the determinant of %28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29 is:


abs%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29=%283%29%288%2F3%29-%282%29%284%29=8-8=0

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Answer:

So abs%28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29=0 which means that the determinant of the matrix %28matrix%282%2C2%2C3%2C4%2C2%2C8%2F3%29%29 is 0