Register

TIFR Mathematics 2022 | Part B | Question: 7

• edited by
207 views
1 votes
1 votes

Answer whether the following statements are True or False.

There exists $A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right) \in \mathrm{M}_{2}(\mathbb{R})$, with $A^{2}=A \neq 0$, such that

$$|a|+|b|<1 \quad \text{and} \quad|c|+|d|<1.$$

• edited by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
1 answer
1
admin asked Sep 9, 2022
458 views
TIFR Mathematics 2022 | Part B | Question: 1
Answer whether the following statements are True or False. $\mathbb{R}^{2} \backslash \mathbb{Q}^{2}$ is connected but not path-connected.
Answer whether the following statements are True or False.$\mathbb{R}^{2} \backslash \mathbb{Q}^{2}$ is connected but not path-connected.
User Avatar
1 votes
1 votes
0 answers
2
admin asked Sep 9, 2022
327 views
TIFR Mathematics 2022 | Part B | Question: 2
Answer whether the following statements are True or False. If $X$ is a connected metric space, and $F$ is a subring of $C(X, \mathbb{R})$ that is a field, then every element of $C(X, \mathbb{R})$ that belongs to $F$ is a constant function.
Answer whether the following statements are True or False.If $X$ is a connected metric space, and $F$ is a subring of $C(X, \mathbb{R})$ that is a field, then every eleme...
User Avatar
1 votes
1 votes
0 answers
3
admin asked Sep 9, 2022
305 views
TIFR Mathematics 2022 | Part B | Question: 3
Answer whether the following statements are True or False. Let $K \subseteq[0,1]$ be the Cantor set. Then there exists no injective ring homomorphism $C([0,1], \mathbb{R}) \rightarrow C(K, \mathbb{R})$.
Answer whether the following statements are True or False.Let $K \subseteq[0,1]$ be the Cantor set. Then there exists no injective ring homomorphism $C([0,1], \mathbb{R})...
User Avatar
1 votes
1 votes
0 answers
4
admin asked Sep 9, 2022
282 views
TIFR Mathematics 2022 | Part B | Question: 4
Answer whether the following statements are True or False. There exists a metric space $(X, d)$ such that the group of isometries of $X$ is isomorphic to $\mathbb{Z}$.
Answer whether the following statements are True or False.There exists a metric space $(X, d)$ such that the group of isometries of $X$ is isomorphic to $\mathbb{Z}$.
User Avatar
Link Copied!