State a pair of values from p and q

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richiesmasher

Junior Member
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T is the matrix

\begin{bmatrix}
2q &0 \\
p& p
\end{bmatrix}

They asked to find the determinant of T which I did and that is 2pq.

Then they said, if q= 1/2 and p=4, find the inverse of T which i did and it is

\begin{bmatrix}
1 &0 \\
-1& 1/4
\end{bmatrix}

Now the question states: ''If T is singular and p is not equal to q, state a pair of values from p and q.

All I know is that singular means the determinant of T equal to 0.

I don't understand what I'm supposed to do here, am I supposed to just guess a random pair of numbers?

If I could do that I would just say 0,0... but then I just realized I can't do that.... as they give the condition... ahhh please help :(

Edit: Actually since the determinant in itself is 2qp, can I just say q= 1 and p = 0 thus giving me 2(0)=0 showing that the matrix is singular?
 
Last edited:
richiesmasher said:
T is the matrix

\begin{bmatrix}
2q &0 \\
p& p
\end{bmatrix}

They asked to find the determinant of T which I did and that is 2pq.

Then they said, if q= 1/2 and p=4, find the inverse of T which i did and it is

\begin{bmatrix}
1 &0 \\
-1& 1/4
\end{bmatrix}

Now the question states: ''If T is singular and p is not equal to q, state a pair of values from p and q.

All I know is that singular means it's equal to 0.

I don't understand what I'm supposed to do here, am I supposed to just guess a random pair of numbers?

If I could do that I would just say 0,0... but then I just realized I can't do that.... as they give the condition... ahhh please help :(

Edit: Actually since the determinant in itself is 2qp, can I just say q= 1 and p = 0 thus giving me 2(0)=0 showing that the matrix is singular?
Click to expand...

All I know is that singular means it's equal to 0 What on earth does it mean? Be clear and say what you mean.
If a 2x2 matrix is singular then it means the determinant of the matrix is 0.

So the determinant 2pq=0. Well find some numbers for p and q so that 2pq=0 and don't pick the same number for p and q.
Hint: when is a product of three numbers equal to 0?? (note: 2pq is a product of three numbers)
 
Jomo said:
All I know is that singular means it's equal to 0 What on earth does it mean? Be clear and say what you mean.
If a 2x2 matrix is singular then it means the determinant of the matrix is 0.

So the determinant 2pq=0. Well find some numbers for p and q so that 2pq=0 and don't pick the same number for p and q.
Hint: when is a product of three numbers equal to 0?? (note: 2pq is a product of three numbers)
Click to expand...

A product of three numbers is equal to zero when one of the numbers is 0, so p can be 0 and q can be 1
 
Last edited:
richiesmasher said:
A product of three numbers is equal to zero when one of the numbers is 0
Click to expand...
Not exactly true. At least one must be 0. That is exactly one number could be 0 or exactly two of the numbers could be 0 or all three numbers could be 0.
So can you give values for p and q so the determinant is 0 and p and q are not the same number?
 
Jomo said:
Not exactly true. At least one must be 0. That is exactly one number could be 0 or exactly two of the numbers could be 0 or all three numbers could be 0.
So can you give values for p and q so the determinant is 0 and p and q are not the same number?
Click to expand...

Yes, p=0, q=1
 
Jomo said:
Seems good to me. You do know that there are MANY other answers, correct??
Click to expand...

Yes I know, i just was caught off guard by such an ambiguous question, so i thought there must be a formula, but then I realized it is a matrices worksheet so perhaps they are testing just knowledge of things like singular non singular etc, and the values of p and q don't matter once they remain true to the matrix's singularity
 
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