Register

TIFR2010-Maths-B-2

• edited by
2,682 views
3 3 votes

If $V$ is a vector space over the field $\mathbb{Z}/5\mathbb{Z}$ and $\dim_{Z/5\mathbb{Z}}(V)=3$ then $V$ has.

  1. 125 elements
  2. 15 elements
  3. 243 elements
  4. None of the above

1 Answer

Best answer
3 3 votes
Field $\mathbb{Z}/5\mathbb{Z}$ means set of integers modulo 5 i.e. this field is $\{0,1,2,3,4\}$.

So vector over this field will contain elements from set $\{0,1,2,3,4\}$ only.

Dimension of each vector is 3 i.e. a vector is a 3-tuple where each element is from $\{0,1,2,3,4\}$.

So for each element in 3-tuple, we have 5 choices, hence total number of vectors is $5*5*5=125$.
• edited by
Voting & Accepting an answer helps improve the community
← Previous · TIFR2010-Maths-B-1Next → · TIFR2010-Maths-B-3
← Previous in category · TIFR2010-Maths-A-10Next in category → · TIFR2010-Maths-B-10
Position:
Show:

Related questions

7 7 votes
1 answers 1 answer
1.4k
1.4k views
Misbah Ghaya asked Oct 15, 2015
1,420 views
TIFR2010-Maths-B-14
The equations.$x_{1}+2x_{2}+3x_{3}=1$$x_{1}+4x_{2}+9x_{3}=1$$x_{1}+8x_{2}+27x_{3}=1$haveOnly one solutionTwo solutionsInfinitely many solutionsNo solutions
2 2 votes
1 answers 1 answer
1.1k
1.1k views
Misbah Ghaya asked Oct 14, 2015
1,093 views
TIFR2010-Maths-B-11
Which of the following is true?The matrix $\begin{pmatrix}1&0 \\1&2\end{pmatrix}$ is not diagonalisableThe matrix $\begin{pmatrix}1&5 \\0&2\end{pmatrix}$ is diagonalisabl...
3 3 votes
1 answers 1 answer
2.9k
2.9k views
Misbah Ghaya asked Oct 14, 2015
2,887 views
TIFR2010-Maths-B-10
Let $x$ and $y \in \mathbb{R}^{n}$ be non-zero column vectors, from the matrix $A=xy^{T}$, where $y^{T}$ is the transpose of $y$. Then the rank of $A$ is:$2$$0$At least $...
5 5 votes
2 answers 2 answers
2.0k
2.0k views
Misbah Ghaya asked Oct 11, 2015
1,977 views
TIFR2010-Maths-A-10
Let $M_{n}(R)$ be the set of n x n matrices with real entries. Which of the following statements is true?Any matrix $A \in M_{4}(R)$ has a real eigenvalueAny matrix $A \i...