Question:medium
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Let $A = \begin{bmatrix} 3 & 0 & -1 \\ 3 & 0 & -1 \\ 4 & 0 & 5 \end{bmatrix}$, then $\text{Nullity}(A) = 1, \text{Rank}(A) = 2$.
Reason R : For a linear transformation $T: \mathbb{R}^n \to \mathbb{R}^n$, $\text{Rank}(T) + \text{Nullity}(T) \neq n$.
In the light of the above statements, choose the correct answer from the options given below
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Let $A = \begin{bmatrix} 3 & 0 & -1 \\ 3 & 0 & -1 \\ 4 & 0 & 5 \end{bmatrix}$, then $\text{Nullity}(A) = 1, \text{Rank}(A) = 2$. Reason R : For a linear transformation $T: \mathbb{R}^n \to \mathbb{R}^n$, $\text{Rank}(T) + \text{Nullity}(T) \neq n$. In the light of the above statements, choose the correct answer from the options given below
Assertion A : Let $A = \begin{bmatrix} 3 & 0 & -1 \\ 3 & 0 & -1 \\ 4 & 0 & 5 \end{bmatrix}$, then $\text{Nullity}(A) = 1, \text{Rank}(A) = 2$. Reason R : For a linear transformation $T: \mathbb{R}^n \to \mathbb{R}^n$, $\text{Rank}(T) + \text{Nullity}(T) \neq n$. In the light of the above statements, choose the correct answer from the options given below
Show Hint
Rank-Nullity Theorem is an equality: $\text{Rank}(T) + \text{Nullity}(T) = n$. Any assertion claiming $\neq n$ is immediately false!
Updated On: Jul 30, 2026
- Both A and R are true and R is the correct explanation of A
- Both A and R are true but R is NOT the correct explanation of A
- A is true but R is false
- A is false but R is true
Show Solution
The Correct Option is C
Solution and Explanation
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