v1 = (2 -1 2 1)v2 = (0 -1 1 -3) These vectors are column vectors.

Find a 2x4 matrixA, with linearly independent rows, such thatAv1 =0andAv2 =0.

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- Feb 28th 2011, 08:57 PMskittleConstruct a matrix
**v**1 = (2 -1 2 1)**v**2 = (0 -1 1 -3) These vectors are column vectors.

Find a 2x4 matrix*A*, with linearly independent rows, such that*A***v**1 =**0**and*A***v**2 =**0**. - Mar 1st 2011, 01:10 AMFernandoRevilla
A basis of with the usual inner product provides the rows of .

- Mar 1st 2011, 04:46 AMHallsofIvy
Or, find a, b, c, d, e, f, g, h such that

and

That gives you four equations to solve for 8 values. Of course, there will be an infinite number of such matrices just as there are an infinite number of possible bases for the orthogonal space FernandoRevilla suggests. - Mar 1st 2011, 05:26 AMFernandoRevilla
- Mar 2nd 2011, 08:35 AMskittle
Thanks so much for the help!

I was just wondering what does the thing the looks like an upside down T by the (v1, v2) mean? - Mar 2nd 2011, 09:19 AMFernandoRevilla