Question

If A is any mxn matrix then çank(A) + dim Nul (A)=
​

Answer 1

Step-by-step explanation:

Rank of a matrix is the dimension of the column space. Rank Theorem : If a matrix "A" has "n" columns, then dim Col A + dim Nul A = n and Rank ... There are no pivots in columns 3 and 5.

Answer 2

Answer:

Rank(A) + dim Nul(A) = the number of columns of A (n)

Step-by-step explanation:

If A is any m × n matrix, then

The dimension of its column space or row space is called the rank of A

The dimension of its null space is called as nullity of A

The connection between these two dimensions is given by the rank nullity theorem that is,

Rank(A) + dim Nul(A) = the number of columns of A (n)

Therefore Rank(A) + dim Nul(A) = the number of columns of A