Recent questions in Engineering Mathematics / GATE Overflow for GATE CSE

2 votes

1 answer

21

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 15
The matrix $ \left(\begin{array}{rr} -2 & 11 \\ 4 & 2 \end{array}\right) $ represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{rr}-2 & 11 \\ 4 & 2\end{array}\right)$

The matrix$$\left(\begin{array}{rr}-2 & 11 \\4 & 2\end{array}\right)$$represents a linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ with respect to th...

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GO Classes asked Apr 11

4 votes

1 answer

22

GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 16
Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$ ... the matrix equation $A x=0$ has infinitely many solutions, then $\operatorname{rank}(A) \leq 4$.

Suppose $A$ is an $11 \times 5$ matrix and $T$ is the corresponding linear transformation given by the formula $T(x)=A x$. Which of the following statements are true?$\op...

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44 views

GO Classes asked Apr 11

1 votes

1 answer

23

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 1
If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then $A=\phi$ $B=\phi$ $A\neq B$ $A=B$

If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then$A=\phi$$B=\phi$$A\neq B$$A=B$

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GO Classes asked Apr 10

1 votes

2 answers

24

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 2
The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?

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63 views

GO Classes asked Apr 10

2 votes

1 answer

25

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 3
What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ? $\{(1, a),(1, b),(2, a),(b, b)\}$ $\{(1,1),(2,2),(a, a),(b, b)\}$ $\{(1, a),(2, a),(1, b),(2, b)\}$ $\{(1,1),(a, a),(2, a),(1, b)\}$

What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ?$\{(1, a),(1, b),(2, a),(b, b)\}$$\{(1,1),(2,2),(a, a),(b, b)\}$$\{(1, a),(2, a),(1, b),(2, b)\}$$\{(1,1),(...

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GO Classes asked Apr 10

3 votes

1 answer

26

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 4
Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then $2^{|A|} \leq|B|$ $2^{|A|} \geq|B|$ $2|A|<|B|$ $2^{|A|} \geq 2^{|B|}$

Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then$2^{|A|} \leq|B|$$2^{|A|} \geq|B|$$2|A|<|B|$$2^{|A|} \geq 2^{|B|}$

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61 views

GO Classes asked Apr 10

2 votes

3 answers

27

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 5
Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is: $2^{n^2}$ $\left(2^n\right)^2$ $\left(2^2\right)^n$ None of the above

Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is:$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of...

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62 views

GO Classes asked Apr 10

1 votes

1 answer

28

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 6
Which one of the following is/are true? $R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$ $R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$ $R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$ $R \cap S=(R \cup S) \cup(R-S)$

Which one of the following is/are true?$R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$$R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$$R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$$R \cap S=(R \...

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43 views

GO Classes asked Apr 10

3 votes

1 answer

29

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 7
Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasing size ? $|A-B|<|A \oplus B|<|A|+|B|<|A \cup B|$ ... $|A-B|<|A \oplus B|<|A \cup B|<|A|+|B|$

Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasi...

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73 views

GO Classes asked Apr 10

5 votes

1 answer

30

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 8
Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is listed in lexicographic order, then the next element after $((1,0), c,(1,1))$ is $((1,0), a,(0,0))$ $((1,1), c,(0,0))$ $((1,1), a,(0,0))$ $((1,1), a,(1,1))$

Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is...

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86 views

GO Classes asked Apr 10

3 votes

0 answers

31

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 9
Which of the following statements is $\textbf{TRUE}$? For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$. For all sets $A, B$, and $C,(A-B) \cap(C-B)=A-(B \cup C)$. For all sets $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.

Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all sets ...

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61 views

GO Classes asked Apr 10

1 votes

0 answers

32

GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 10
Which of the following statements is $\textbf{FALSE}$? $C-(B \cup A)=(C-B)-A$ $A-(C \cup B)=(A-B)-C$ $B-(A \cup C)=(B-C)-A$ $A-(B \cup C)=(B-C)-A$

Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$$A-(C \cup B)=(A-B)-C$$B-(A \cup C)=(B-C)-A$$A-(B \cup C)=(B-C)-A$

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52 views

GO Classes asked Apr 10

0 votes

1 answer

33

Internet
A non empty set A is termed as an algebraic structure ________ a)with respect to binary operation * b)with respect to ternary operation ? c)with respect to binary operation + d)with respect to unary operation –

A non empty set A is termed as an algebraic structure ________a)with respect to binary operation *b)with respect to ternary operation ?c)with respect to binary operation ...

Tankut

80 views

Tankut asked Apr 4

6 votes

2 answers

34

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 1
Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”? The columns of $A$ are linearly independent. The rows of $A$ are linearly independent. The only solution of the homogeneous equations $Ax = 0$ is $x = 0$. The rank of $A$ is $n$.

Let $A$ be an $n \times n$ matrix of real or complex numbers. Which of the following statements are equivalent to: “the matrix $A$ is invertible”?The columns of $A$ a...

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94 views

GO Classes asked Apr 3

7 votes

3 answers

35

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 2
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant $c$. Which (if any) any of the vectors must be an eigenvector of $M$ ... $W = \left[\begin{array}{l}1 \\ 1 \\ \end{array}\right]$ $U$ $V$ $W$ None of the above

Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rowsand also the sum of each of the columns is the same constant $c$. Which (if any) any of...

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135 views

GO Classes asked Apr 3

3 votes

1 answer

36

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 3
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$. Which of the following statements are true for matrix $A$. $-v$ is an eigenvector of $-A$ with eigenvalue $- \lambda$. If $v$ is also ... $A+B$. eigenvalue of $A^3$ is $\lambda^3$ and the eigenvector is $v^3$ .

Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$.Which of the following statements are true for matrix $A$.$-v$ is an eigen...

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130 views

GO Classes asked Apr 3

1 votes

2 answers

37

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 4
Consider the following matrix A: $\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$ Which of the following regarding the matrix $A$ ... $x$ is the eigenvector corresponding to eigenvalue $\lambda$ of $A$ then $x$ is also the eigenvector of $A^{-1}$.

Consider the following matrix A:$\left[\begin{array}{lll}2 & -1 & 0 \\ 0 & 2 & 0 \\ 1 & 0 & 2\end{array}\right]$Which of the following regarding the matrix $A$ is/are cor...

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82 views

GO Classes asked Apr 3

1 votes

1 answer

38

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 5
Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$ ... BLANK 2: Infinitely many solutions BLANK 1: Sometimes, BLANK 2: Unique solution BLANK 1: Sometimes, BLANK 2: Infinitely many solutions

Suppose a $3 \times 5$ matrix $A$ has rank $r = 3$. Then the equation $Ax = b$ $\textbf{BLANK 1}$ has $\textbf{BLANK 2}$.Which of the following are appropriate words ...

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50 views

GO Classes asked Apr 3

3 votes

2 answers

39

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 6
Which of the following statements is/are $\textbf{NOT CORRECT}$? If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue. If $A$ is a nilpotent matrix, meaning that $A^k = 0$ for the ... is an eigenvalue of an invertible matrix $A$ then $\lambda ^{-1}$ is an eigenvalue of $A^{-1}$.

Which of the following statements is/are $\textbf{NOT CORRECT}$?If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue.If ...

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90 views

GO Classes asked Apr 3

2 votes

1 answer

40

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 7
Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any $b$ is consistent. $S2:$ $Ax = b$ always has a unique solution. ... $S2$ is FALSE. $S1$ is FALSE and $S2$ is TRUE. Both $S1$ and $S2$ are FALSE.

Given an $m \times n$ matrix $A$ whose rows are linearly independent. Now, consider following statements regarding $A$: $S1:$ The system of equations $Ax = b$ for any ...

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GO Classes asked Apr 3

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