Math Is Fun Forum

mathsforumhelp

Member

Registered: 2009-10-07

Posts: 14

Maths

Let A be the matrix
3 2 2 -3
-6 -6 -7 3
-12 0 4 26
-9 -10 -12 -3
1. A basis for the row space of A is________
    Are the row vectors of A linearly independent?
    The rank of A is_______and the nullity of A is_________
2. Is the row space of A equal to R4?
    Does the system Ax = 0 have only the trivial solution?
    Is the matrix A invertible?
3. A basis for the column space of A is____________
    Are the column vectors of A linearly independent?
    The rank of AT is______and the nullity of AT is_______
4. Is the column space of A equal to R4?
    Does the system ATx = 0 have only the trivial solution?
    Is the matrix AT invertible?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maths

Hi mathsforumhelp;

2) is the matrix A invertible?

No, the matrix is singular so it is not invertible.

4) is the transpose of matrix A invertible?

I believe when the determinant of A is 0 , the determinant of the transpose of A is 0. But I have computed it to be sure.

So the transpose is not invertible.

Last edited by bobbym (2009-10-13 15:38:49)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathsforumhelp

Member

Registered: 2009-10-07

Posts: 14

Re: Maths

good answer thanks very much