Recent questions tagged goclasses2025_csda_wq3 / GATE Overflow for GATE CSE

4 votes

1 answer

1

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 1
What will be the value of the following expression? $ \frac{1}{\log _a a b c}+\frac{1}{\log _b a b c}+\frac{1}{\log _c a b c} $

What will be the value of the following expression?$$\frac{1}{\log _a a b c}+\frac{1}{\log _b a b c}+\frac{1}{\log _c a b c}$$

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GO Classes asked Mar 14, 2023

16 votes

2 answers

2

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 2
If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

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GO Classes asked Mar 14, 2023

6 votes

4 answers

3

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 3
Let us consider the following three vectors $v_1, v_2,$ and $v_3$ in $\mathbb{R}^3$ ... $\left\{v_1, v_3\right\}$ are linearly independent.

Let us consider the following three vectors $v_1, v_2,$ and $v_3$ in $\mathbb{R}^3$.$$\begin{aligned}& v_1=\left(\begin{array}{lll}1 & 0 & -2\end{array}\right) \\& v_2=\l...

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GO Classes asked Mar 14, 2023

5 votes

3 answers

4

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 4
Let $a, b$ be in $\mathbb{R}$ ... and $b=1$ $a \neq 0$ and $b \neq 1$ $a=0$ and $b \neq 1$ $a \neq 0$ and $b=1$

Let $a, b$ be in $\mathbb{R}$. Consider the three vectors$$\boldsymbol{v}_1=\left[\begin{array}{l}a \\0 \\0\end{array}\right], \quad \boldsymbol{v}_2=\left[\begin{array}{...

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GO Classes asked Mar 14, 2023

8 votes

3 answers

5

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 5
Which of the following is FALSE? If $v_1, \ldots, v_4$ are in $\mathbf{R}^5$ and $\left\{v_1, v_2, v_3\right\}$ is linearly dependent then $\left\{v_1, v_2, v_3, v_4\right\}$ is linearly dependent. ... $6$ vectors in $\mathbf{R}^5$ is linearly dependent.

Which of the following is FALSE?If $v_1, \ldots, v_4$ are in $\mathbf{R}^5$ and $\left\{v_1, v_2, v_3\right\}$ is linearly dependent then $\left\{v_1, v_2, v_3, v_4\right...

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GO Classes asked Mar 14, 2023

12 votes

2 answers

6

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 6
Consider a set of $n$ linearly independent vectors $\left\{\vec{w}_1, \ldots, \vec{w}_n\right\} \in \mathbb{R}^n$. A vector $\vec{u} \in \mathbb{R}^n$ will: Option $1.$ Always be a linear ... $2$ is correct then enter $\text{ 2 }.$

Consider a set of $n$ linearly independent vectors $\left\{\vec{w}_1, \ldots, \vec{w}_n\right\} \in \mathbb{R}^n$. A vector $\vec{u} \in \mathbb{R}^n$ will:Option $1.$ Al...

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781 views

GO Classes asked Mar 14, 2023

9 votes

3 answers

7

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 7
Which of the following set is/are linearly independent? $\left\{\left[\begin{array}{l}1 \\ 2\end{array}\right],\left[\begin{array}{l}2 \\ 1\end{array}\right]\right\}$ ...

Which of the following set is/are linearly independent?$\left\{\left[\begin{array}{l}1 \\ 2\end{array}\right],\left[\begin{array}{l}2 \\ 1\end{array}\right]\right\}$ $\le...

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832 views

GO Classes asked Mar 14, 2023

11 votes

7 answers

8

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 8
$a\left[\begin{array}{l}1 \\ 2 \\ 3 \\ 4 \\ 5\end{array}\right]+b\left[\begin{array}{c}-1 \\ 2 \\ -3 \\ 4 \\ -5\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0 \\ 0 \\ 0\end{array}\right]$ How many number of pairs $(a, b)$ are there, that satisfy the above equation? $0$ $1$ Infinite $2$

$$a\left[\begin{array}{l}1 \\ 2 \\ 3 \\ 4 \\ 5\end{array}\right]+b\left[\begin{array}{c}-1 \\ 2 \\ -3 \\ 4 \\ -5\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0 \\ 0 ...

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GO Classes asked Mar 14, 2023

9 votes

4 answers

9

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 9
Given a set of vectors $\text{S}(|\text{S}| \geq n)$, with all vectors in $\mathbb{R}^n$, which of the following is a necessary and sufficient condition for the vectors of $\text{S}$ to be Linearly ... $u$ can be represented as a linear combination of vectors (other than $u$ ) of the set $\text{S}$.

Given a set of vectors $\text{S}(|\text{S}| \geq n)$, with all vectors in $\mathbb{R}^n$, which of the following is a necessary and sufficient condition for the vectors o...

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774 views

GO Classes asked Mar 14, 2023

21 votes

6 answers

10

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 10
Which of the following is(are) sufficient argument(s) to show that the vectors of set $\text{S}$ ... $7 u+(-1) v+1 w=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$

Which of the following is(are) sufficient argument(s) to show that the vectors of set $\text{S}$ are linearly dependent?$$\text{S}=\left\{u=\left[\begin{array}{c}1 \\-2 \...

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GO Classes asked Mar 14, 2023

16 votes

5 answers

11

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 11
Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$ ... $\text{AX}=\overrightarrow{0}$.

Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$$$\left[\begin{array}{ccc}2 & 3 & -5 \\-5 & -1 & 32 \\2 & -...

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1.2k views

GO Classes asked Mar 14, 2023

8 votes

3 answers

12

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 12
Given a set $\text{S}$ of vectors in $\mathbb{R}^n$, and set $\text{X(X} \subset \text{S})$ and $\text{Y(S} \subset \text{Y}),$ mark all the statements which are always true: If the ... . If the vectors of $\text{S}$ are Linearly Independent, then the vectors of $\text{Y}$ are also Linearly Independent.

Given a set $\text{S}$ of vectors in $\mathbb{R}^n$, and set $\text{X(X} \subset \text{S})$ and $\text{Y(S} \subset \text{Y}),$ mark all the statements which are always t...

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604 views

GO Classes asked Mar 14, 2023

13 votes

4 answers

13

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 13
What will be value of $x$ satisfying the below equation? $ \sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2 $

What will be value of $x$ satisfying the below equation?$$\sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2$$

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843 views

GO Classes asked Mar 14, 2023

10 votes

2 answers

14

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 14
Which of the following is/are CORRECT? $u,v, \text{ and } w$ are vectors in $\mathbb{R}^n$. A set $\{u, v, w\}$ is linearly independent if $ u $ can not be written as linear combination of $v$ ... $\{\mathbf{u}, \mathbf{v}, \mathbf{w}\}$ is linearly independent.

Which of the following is/are CORRECT?$u,v, \text{ and } w$ are vectors in $\mathbb{R}^n$.A set $\{u, v, w\}$ is linearly independent if $ u $ can not be written as linea...

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746 views

GO Classes asked Mar 14, 2023

18 votes

2 answers

15

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 15
$\mathrm{S} 1:$ A set of two vectors in $\mathbb{R}^n$ is Linealy dependent if at least one vector is a multiple of the other. $\text{S2}:$ A set of $n$ vectors in $\mathbb{R}^n$ is Linealy independent if and ... $\text{S} 1$ is incorrect $\text{S} 1$ and $\text{S} 2$ both are incorrect

$\mathrm{S} 1:$ A set of two vectors in $\mathbb{R}^n$ is Linealy dependent if at least one vector is a multiple of the other.$\text{S2}:$ A set of $n$ vectors in $\mathb...

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GO Classes asked Mar 14, 2023

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