If A is 3×3 with rank A=2, show that the dimension of the null space of A is l.

Question

Kayla Kline · Accepted Answer

To solve this question we shall use rank nullity theorem.
$R a n k A + n u l l i t y A =$ no. of columns in A
Solution:
Dimension of null space of $A = n u l l i t y o f A$
no. of columns of $A = 3$
Rank $A = 2$
nullity $A =$ no. of columns in A-rank A
$= 3 - 2$
$= 1$
nullity $A = 1$
dimension of null space $= 1$

Karen Robbins · Accepted Answer

Rank nullity dimension theorem:
For any matrix A, we have

\Rightarrow p + N = Number of coloumns of A

(1)
Where

N =

Dimensional of null space

\Rightarrow p =

rank of matrix A
We have given that for a matrix A of order

3 \times 3

\Rightarrow p = rank(A) = 2

\Rightarrow Number of columns of A = 3

Then from equation (1), we have

\Rightarrow 2 + N = 3

\Rightarrow N = 3 - 2

\Rightarrow N = 1

Dimension of null space

= 1

Vasquez · Accepted Answer

Step 1⇒p+N=Numbe of coloumns of AWhere N= Dimensional of null space⇒p= rank of matrix AWe have given that for a matrix A of order 3×3⇒p=rank (A)=2⇒Number of columns of A=3Step 2⇒2+N=3⇒N=3−2⇒N=1

If A is 3 \times 3 with rank A =

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