[jhomie]

I was revising a few past chapters and I just can't do these matrices questions. I can do some of the other row operations one, but i don't know what to do for these. The book shows the answers (although there are many wrong answers), but it doesn't show how to get the answers.

Any help with how to do these questions will help a lot !

Please if someone could show me how to do these, i really need to know!

Q11.

Q12. (sorry it says 'x,y and z twice'

Q14.

Q15.

Q17.


Please if someone could show me how to do these, i really need to know!

[AEsp]

Just learn the determinant of 3x3 matrices, that should get you through atleast two of them.

[generalebriety]

What? I helped you with these exact questions a week or so ago. Go and find that thread.

[jhomie]

Originally Posted by AEsp

Just learn the determinant of 3x3 matrices, that should get you through atleast two of them.

I've learnt the determinant but can't seem to crack these problems

Originally Posted by generalebriety

What? I helped you with these exact questions a week or so ago. Go and find that thread.

sorry, i was a way for a bit and didn't see the thread. i've looked back at it and thanks for number 11, but i just don't seem to find the right operations to reduce the rows to 0. i might be doing something wrong, but i cant seem to eliminate variables

[generalebriety]

Originally Posted by jhomie

sorry, i was a way for a bit and didn't see the thread. i've looked back at it and thanks for number 11, but i just don't seem to find the right operations to reduce the rows to 0. i might be doing something wrong, but i cant seem to eliminate variables

Post your working, then, please.

[EierVonSatan]

Originally Posted by jhomie

sorry, i was a way for a bit and didn't see the thread. i've looked back at it and thanks for number 11, but i just don't seem to find the right operations to reduce the rows to 0. i might be doing something wrong, but i cant seem to eliminate variables

Gaussian elimination just takes practice - identify the pivots and subtract/add multiples of other rows so that the number under the pivot is zero until it becomes upper triangular form. The solution then becomes trivial

[bruceleej]

Originally Posted by EierVonSatan

Gaussian elimination just takes practice - identify the pivots and subtract/add multiples of other rows so that the number under the pivot is zero until it becomes upper triangular form. The solution then becomes trivial

Quick question, after reducing it to an Upper Triangular; what are the conditions for infinite solutions and no solutions?
Thanks.

[EierVonSatan]

Originally Posted by bruceleej

Quick question, after reducing it to an Upper Triangular; what are the conditions for infinite solutions and no solutions?
Thanks.

You don't need to get into upper triangular form to determine this, if the equations are inconsistent then there are no solutions (determinant is likely zero). For infinite solutions, the equations must first be consistent, often the rows wil be multiples of each other. For a system like Ax = b to be solvable b must be in the column space of A. I think thats how it works anyway

[jhomie]

Originally Posted by EierVonSatan

Gaussian elimination just takes practice - identify the pivots and subtract/add multiples of other rows so that the number under the pivot is zero until it becomes upper triangular form. The solution then becomes trivial

what is a pivot and upper triangle? perhaps it is why i can't do these, but i do know what gaussian elimination is; its in the book before these questions

[EierVonSatan]

Originally Posted by jhomie

what is a pivot and upper triangle? perhaps it is why i can't do these, but i do know what gaussian elimination is; its in the book before these questions

A pivot is the first nonzero element in a row, upper triangular form is zero elements in the lower left hand corner (not including the longest diagonal) for example:



this matrix has three pivots 1, 5 and 9 and is said to have rank 3