Assume that A is row equivalent to B. Find bases for Nul A and Col A.

djeljenike 2021-09-13 Answered

Assume that A is row equivalent to B. Find bases for Nul A and Col A.
A=[12511324515212045365192]
B=[12045005780000900000]

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Expert Answer

BleabyinfibiaG
Answered 2021-09-14 Author has 118 answers

Since B is a row echelon form of A, we see that the first, third and fifth columns of A are its pivot columns. Thus a basis fo Col A is
{[1213],[5505],[3252]}
To find a basis for Nul A, we find the general solution of Ax=0 in terms of the free variables. Since it is row equivalent to B we can simply get reduced row echelon form of B:
[12045005780000900000]R215R2R319R3  [120450057500000100000]
R1R15R3R2R285R3[120450017500000100000]
to get: x1=2x24x4,x3=75x4, x5=0, with x2 and x4 free. So
x=[x1x2x3x4x5]=x2[21000]+x4[407/510]
And a basis for Nul A is
{[21000],[407/510]}
Result: Basis for Col A is:
{[1213],[5505],[3252]}
Basis for Nul A is
{[21000],[407/510]}

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