Question:medium

Two vectors \([2 \, 1 \, 0 \, 3]^T\) and \([1 \, 0 \, 1 \, 2]^T\) belong to the null space of a \(4 \times 4\) matrix of rank 2. Which one of the following vectors also belongs to the null space?

Updated On: Feb 3, 2026

Show Solution

Correct Answer: -1 - 1

Solution and Explanation

Was this answer helpful?

0

Top Questions on Linear Algebra

Let \(n\) be the number obtained on rolling a fair die. If the probability that the system \[ \begin{cases} x - ny + z = 6 \\ x + (n-2)y + (n+1)z = 8 \\ (n-1)y + z = 1 \end{cases} \] has a unique solution is \( \dfrac{k}{6} \), then the sum of \(k\) and all possible values of \(n\) is
- JEE Main - 2026
- Mathematics
- Linear Algebra
View Solution
If the system of linear equations \[ \begin{cases} 3x + y + \beta z = 3 \\ 2x + \alpha y - z = 1 \\ x + 2y + z = 4 \end{cases} \] has infinitely many solutions, then the value of \(22\beta - 9\alpha\) is:
- JEE Main - 2026
- Mathematics
- Linear Algebra
View Solution
If the system of equations
\( 3x + y + 4z = 3 \)
\( 2x + \alpha y - z = -3 \)
\( x + 2y + z = 4 \)
has no solution, then the value of \( \alpha \) is equal to :
- JEE Main - 2026
- Mathematics
- Linear Algebra
View Solution
What is the value of \((AB)^T\) in matrix algebra?
- CUET (PG) - 2026
- Data Science
- Linear Algebra
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in GATE CE exam

A bridge has an expected design life of 50 years. It is designed for a flood discharge of 1000 m\(^3\)/s, which corresponds to a return period of 100 years. Determine the risk (probability) that the design flood will be equalled or exceeded at least once during the design life of the bridge. (Enter the numerical value of risk in decimal form, correct up to three decimal places.)

GATE CE - 2026
Hydrograph

A function f(x) is defined on the interval with values in R. It satisfies \( \int_0^2 f(x)[x-f(x)]dx = \frac{2}{3} \). Find the value of f(1).}

GATE CE - 2026
Calculus

Bag-I contains 4 white and 6 black balls, Bag-II contains 4 white and 3 black balls. A ball is selected at random and it comes out to be a black ball. What is the probability that it is from Bag-I?

GATE CE - 2026
Probability and Statistics

Given the following data: x: (-2, 1, 2), y: (28, 4, 16). Let \(P_2(x)\) be the quadratic interpolating polynomial passing through the above three points. Find the value of \(P_2(0)\).

GATE CE - 2026
Numerical Methods