Trace of matrix

[c4l3b]

Hi,

Come across this exam question and it really got me ticking!

Question

Find the value of c for the matrix


C = \(\displaystyle \begin{pmatrix}3 & 0 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 & 0\\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & c & 0\\ 0 & 0 & 0 & 0 & 1\end{pmatrix}\)


to be singular. Find the value of c for the Trace of matrix C to be 1.
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So If a matrix is singular then its determinant is equal to 0. The determinant is simply the product of the diagonal (in a diagonal matrix).

How do I tackle this question? Any suggestions please?

Thanks

 

[Deleted member 4993]

Hi,

Come across this exam question and it really got me ticking!

Question

Find the value of c for the matrix


C = \(\displaystyle \begin{pmatrix}3 & 0 & 0 & 0 & 0 \\ 0 & 3 & 0 & 0 & 0\\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & c & 0\\ 0 & 0 & 0 & 0 & 1\end{pmatrix}\)


to be singular. Find the value of c for the Trace of matrix C to be 1.
-----------------------------------------------------------------------------------------------------------------------





So If a matrix is singular then its determinant is equal to 0. The determinant is simply the product of the diagonal (in a diagonal matrix). <<< So where are you stuck??
How do I tackle this question? Any suggestions please?

Thanks

Trace of a matrix is the sum of the diagonal elements.

What is the trace of the matrix [C] - in terms of parameter 'c'?

 

[c4l3b]

so C = 1, 3 x 3 x 2 x c x 1?

 

[mmm4444bot]

How do I tackle this question?

There are two questions, in this exercise. (I'm not sure which of these you're asking about.)

To find the value of c that makes the determinant of matrix C zero, solve the following equation for c.

3 * 3 * 2 * c * 1 = 0

To find the value of c that makes the trace of matrix C one, solve the following equation for c.

3 + 3 + 2 + c + 1 = 1

 

[c4l3b]

Re:

How do I tackle this question?

There are two questions, in this exercise. (I'm not sure which of these you're asking about.)

To find the value of c that makes the determinant of matrix C zero, solve the following equation for c.

3 * 3 * 2 * c * 1 = 0

To find the value of c that makes the trace of matrix C one, solve the following equation for c.

3 + 3 + 2 + c + 1 = 1

Could you please show me how to calculate both questions? We have not covered this in our syllabus.

 

[Deleted member 4993]

Re: Re:

How do I tackle this question?

There are two questions, in this exercise. (I'm not sure which of these you're asking about.)

To find the value of c that makes the determinant of matrix C zero, solve the following equation for c.

3 * 3 * 2 * c * 1 = 0

To find the value of c that makes the trace of matrix C one, solve the following equation for c.

3 + 3 + 2 + c + 1 = 1

Could you please show me how to calculate both questions? We have not covered this in our syllabus.

You gotta be kidding!!! This is simple algebra question which a fifth grader should be able to answer.

3 * 3 * 2 * c * 1 = 0

18 * c = 0

c = 0/18 = 0

The next one

3 + 3 + 2 + c + 1 = 1

9 + c = 1

c = 1- 9 = -8

This was covered in your class may be 10 years ago!!!

 

[c4l3b]

Re: Re:

There are two questions, in this exercise. (I'm not sure which of these you're asking about.)

To find the value of c that makes the determinant of matrix C zero, solve the following equation for c.

3 * 3 * 2 * c * 1 = 0

To find the value of c that makes the trace of matrix C one, solve the following equation for c.

3 + 3 + 2 + c + 1 = 1

[/color][/quote]

Could you please show me how to calculate both questions? We have not covered this in our syllabus.[/quote]You gotta be kidding!!! This is simple algebra question which a fifth grader should be able to answer.

3 * 3 * 2 * c * 1 = 0

18 * c = 0

c = 0/18 = 0

The next one

3 + 3 + 2 + c + 1 = 1

9 + c = 1

c = 1- 9 = -8

This was covered in your class may be 10 years ago!!![/quote]

Subhotosh Khan - thanks for the encouragement :roll:

 

[Deleted member 4993]

Re: Re:

You gotta be kidding!!! This is simple algebra question which a fifth grader should be able to answer.

[quote:1iym8lch]We have not covered this in our syllabus.

This was covered in your class may be 10 years ago!!!

Subhotosh Khan - thanks for the encouragement :roll:[/quote:1iym8lch]

Truth is always encouraging - no false pretentions......