What Determines the Rank and Dimension of a Matrix's Solution Space?

[dylanpuw]

(a)Determine the row rank of the matrix,

1 1 1 1
1 1 2 5
2 2 0 -6

(b) What is the column rank of this matrix?
(c) What is the dimension of the solution space Mx=0

So this is my answer:

I have reduced my matrix into echelon form and i get

1 1 1 1
0 0 -1 -4
0 0 0 0

Therefore my row rank is 2 (the number of linearly independent rows)

Since by rank theorem, (row rank = column rank = determinental rank) the column rank is also 2.

And the dimension of the solution space is 2 (number of columns - rank)

Is this answer correct?

Thank you
Dylan

 

[n.karthick]

yes, i think so