a few questions(adsbygoogle = window.adsbygoogle || []).push({});

a) can a 3x4 matrix have independant columns? rows? Explain

if i were to reduce to row echelon form then i could potentially have 4 leading 1s. I m not quite sure about this.

if i were to reduce this 3 x 4 matrix into row echelon form then the number of rows is less than the number of variables. SO the answer is no.

b) if A is a 4 x3 matrix and rank A = 2, can A have independant columns? rows? Explain

ok rank A means that out of the 4 rows only 2 are non zero when A is in row echelon form. Potentially 3 leading 1s in the columns so at least 2 of the columns may be dependant on each other. So independant columns are not possible.

Indepednat rows not possible.

c) Can a non square matrix has its rows indepedant and its columns independant?

im not sure about this. If A (MxN) then for m rows A has n unknowns so it is not possible to have indepdnatn rows. As for the columns i ahve no idea.

If A is m x n and B is n x m show taht AB = 0 iff [itex] col B \subseteq null A [/itex]

suppose AB = 0

let columns of B = [itex]C_{i}[/itex]

rows of A = [itex]R_{i}[/itex]

for all i

then [tex] R_{i} C_{i} = 0 [/itex] if Ci = 0 for all i. Thus Ci belongs to null A

Suppose [tex] col B \subseteq null A [/tex]

then anything times a column of B is zero. Thus AB = 0

Is this proof adequate?

your input is greatly appreciated!

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# Homework Help: Linear Algebra and matrix

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