>
Exams
>
Linear Algebra
>
Matrices
>
let w be the subspace of m 3 consisting of all mat
Question:
Let W be the subspace of
\(M_3(\R)\)
consisting of all matrices with the property that the sum of the entries in each row is zero and the sum of the entries in each column is zero. Then the dimension of W is equal to ___________.
IIT JAM MA - 2023
IIT JAM MA
Updated On:
Oct 1, 2024
Hide Solution
Verified By Collegedunia
Correct Answer:
4
Solution and Explanation
The correct answer is 4.
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Matrices
If
\(A = \begin{bmatrix} 3 & 2 \\ -1 & 1 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} -1 & 0 \\ 2 & 5 \\ 3 & 4 \end{bmatrix},\)
then \((BA)^T\) is equal to:
CUET (UG) - 2024
Mathematics
Matrices
View Solution
If \( A = \begin{bmatrix} K & 4 \\ 4 & K \end{bmatrix} \) and \( |A^3| = 729 \), then the value of \( K^8 \) is:
CUET (UG) - 2024
Mathematics
Matrices
View Solution
Let $A$ be a matrix such that $A^2 = I$, where $I$ is an identity matrix. Then $(I + A)^4 - 8A$ is equal to:
CUET (UG) - 2024
Mathematics
Matrices
View Solution
Let $A = I_2 - MM^T$, where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M = I_1$ holds. If $\lambda$ is a real number such that the relation $AX = \lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$, then the sum of squares of all possible values of $\lambda$ is equal to:
JEE Main - 2024
Mathematics
Matrices
View Solution
Let the system of equations \[x + 2y + 3z = 5, \quad 2x + 3y + z = 9, \quad 4x + 3y + \lambda z = \mu\]have an infinite number of solutions. Then $\lambda + 2\mu$ is equal to:
JEE Main - 2024
Mathematics
Matrices
View Solution
View More Questions
Questions Asked in IIT JAM MA exam
For n ≥ 3, let a regular n-sided polygon P
n
be circumscribed by a circle of radius R
n
and let r
n
be the radius of the circle inscribed in P
n
. Then
\(\lim\limits_{n \rightarrow \infin}(\frac{R_n}{r_n})^{n^2}\)
equals
IIT JAM MA - 2024
Sequences and Series
View Solution
Consider the function f: ℝ → ℝ given by f(x) = x
3
- 4x
2
+ 4x - 6.
For c ∈ ℝ, let
\(S(c)=\left\{x \in \R : f(x)=c\right\}\)
and |S(c)| denote the number of elements in S(c). Then, the value of
|S(-7)| + |S(-5)| + |S(3)|
equals _________
IIT JAM MA - 2024
Functions of One Real Variable
View Solution
For a > b > 0, consider
\(D=\left\{(x,y,z) \in \R^3 :x^2+y^2+z^2 \le a^2\ \text{and } x^2+y^2 \ge b^2\right\}.\)
Then, the surface area of the boundary of the solid D is
IIT JAM MA - 2024
Functions of Two or Three Real Variables
View Solution
Let
S = {f: ℝ → ℝ ∶ f is a polynomial and f(f(x)) = (f(x))
2024
for x ∈ ℝ}.
Then, the number of elements in S is _____________
IIT JAM MA - 2024
Functions of One Real Variable
View Solution
The value of
\(\lim\limits_{t→\infin}\left((\log(t^2+\frac{1}{t^2}))^{-1} \int\limits_{1}^{\pi t} \frac{\sin^25x}{x}dx\right)\)
equals ___________ (rounded off to two decimal places).
IIT JAM MA - 2024
Integral Calculus
View Solution
View More Questions