Recent questions tagged system-of-equations / GATE Overflow for GATE CSE

9 votes

4 answers

31

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 6
If $\text{A}$ is a $4 \times 3$ matrix and $\text{A} x=b$ is not solvable for some $b$ and the solutions are not unique when they exist, possible values for the rank of $\text{A}$ are ________ (list all possibilities). $0$ $1$ $2$ $3$

If $\text{A}$ is a $4 \times 3$ matrix and $\text{A} x=b$ is not solvable for some $b$ and the solutions are not unique when they exist, possible values for the rank of $...

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1.1k views

GO Classes asked Apr 5, 2023

14 votes

1 answer

32

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 7
$A x=b$ has solutions $x_1=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)$ and $x_2=\left(\begin{array}{l}4 \\ 5 \\ 6\end{array}\right)$, and possibly other solutions, for some (real) matrix $A$ and right-hand side $b$. Which of the ... $\left(\begin{array}{l} 4 \\ 4 \\ 4\\ \end{array} \right)$

$A x=b$ has solutions $x_1=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)$ and $x_2=\left(\begin{array}{l}4 \\ 5 \\ 6\end{array}\right)$, and possibly other solution...

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694 views

GO Classes asked Apr 5, 2023

17 votes

1 answer

33

GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 19
Suppose that we are solving $A x=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)$ In each of the option below, a complete solution $x$ is proposed. Which of the following could possibly be the solution for above system of linear ... $\alpha \in \mathbb{R}$

Suppose that we are solving $A x=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)$In each of the option below, a complete solution $x$ is proposed.Which of the followi...

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1.1k views

GO Classes asked Apr 5, 2023

10 votes

2 answers

34

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 5
Consider the system below, where $h$ and $k$ are real numbers. $ \begin{array}{r} x+3 y=2 \\ 3 x-h y=k \end{array} $ Find the values of $h$ and $k$ which give the system infinitely many solutions. $h=-9$ and $k \neq 6$ $h \neq-9$ and $k$ can be any real number $h=-9$ and $k=6$ System is inconsistent for all values of $h$ and $k$

Consider the system below, where $h$ and $k$ are real numbers.$$\begin{array}{r}x+3 y=2 \\3 x-h y=k\end{array}$$Find the values of $h$ and $k$ which give the system infin...

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529 views

GO Classes asked Mar 29, 2023

14 votes

3 answers

35

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 8
Which of the following is/are TRUE? If the echelon form of an $m \times n$ matrix has a pivot in every column then $n \geq m$ If the echelon form of an $m \times n$ matrix $A$ has a pivot in every ... solution. If a system of $25$ linear equations in $13$ unknowns has at least one solution then it has infinitely many solutions.

Which of the following is/are TRUE?If the echelon form of an $m \times n$ matrix has a pivot in every column then $n \geq m$If the echelon form of an $m \times n$ matrix ...

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1.2k views

GO Classes asked Mar 29, 2023

10 votes

2 answers

36

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 10
The given system has infinitely many solutions for $k=?$ $ \left[\begin{array}{ccc} 2 & 2 & -4 \\ 1 & 3 & -2 \\ -4 & k & 8 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{c} 3 \\ 4 \\ -6 \end{array}\right] $

The given system has infinitely many solutions for $k=?$ $$\left[\begin{array}{ccc}2 & 2 & -4 \\1 & 3 & -2 \\-4 & k & 8\end{array}\right]\left[\begin{array}{l}x \\y \\z\e...

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741 views

GO Classes asked Mar 29, 2023

9 votes

2 answers

37

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 11
In the echelon form of the augmented matrix $[A \mid b]:$ A single row of the form $(000 \ldots 0 \mid 0)$ ... have no solution. Only I is true. Only Il is true. Both I and II are true. Neither I, nor II are true.

In the echelon form of the augmented matrix $[A \mid b]:$ A single row of the form $(000 \ldots 0 \mid 0)$ is enough to conclude that the system will have infinitely many...

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816 views

GO Classes asked Mar 29, 2023

8 votes

1 answer

38

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 16
Let $A=\left[\begin{array}{cc}1 & 0 \\ -1 & 1 \\ k & 2\end{array}\right]$ and $b=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]$. For which value of $k$ does the system $A \mathbf{x}=b$ have a unique solution? There is no such value for $k$. $k=0$ $k=-1$ $k=1$

Let $A=\left[\begin{array}{cc}1 & 0 \\ -1 & 1 \\ k & 2\end{array}\right]$ and $b=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]$. For which value of $k$ does the sys...

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930 views

GO Classes asked Mar 29, 2023

10 votes

1 answer

39

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 19
Let $A$ be a $2 \times 3$-matrix and $b$ a vector in $\mathbb{R}^2$. Consider the following two statements: $(\text{P}1)\; A$ has at most two pivots, $(\text{P2})$ Assuming $A x=b$ has a solution, then it ... $\text{P1}$ is correct. Statement $\text{P1}$ and Statement $\text{P2}$ are correct.

Let $A$ be a $2 \times 3$-matrix and $b$ a vector in $\mathbb{R}^2$.Consider the following two statements:$(\text{P}1)\; A$ has at most two pivots,$(\text{P2})$ Assuming ...

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601 views

GO Classes asked Mar 29, 2023

20 votes

3 answers

40

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 20
Suppose $A$ is $3$ by $4,$ and $A x=0$ ... $a, b, c,$ and $d?$ $a=-1$ $b=2$ $c=-1$ $d=1$

Suppose $A$ is $3$ by $4,$ and $A x=0$ has all solutions in the following form -$$\mathrm{x}=\mathrm{s}\left[\begin{array}{l}1 \\1 \\1 \\0\end{array}\right]+\mathrm{t}\le...

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962 views

GO Classes asked Mar 29, 2023

13 votes

2 answers

41

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 21
Consider a matrix $A$ of dimension $m \times n$ such that - $A x=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ has no solutions and $A x=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]$ has exactly one solution Which of the following CAN be true? $\operatorname{Rank}(A)=2$ $m=3$ $n=1$ $\operatorname{Rank}(A)=1$

Consider a matrix $A$ of dimension $m \times n$ such that -$A x=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ has no solutions and $A x=\left[\begin{array}{l}0 \\ ...

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979 views

GO Classes asked Mar 29, 2023

27 votes

2 answers

42

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 23
Let $A$ be an $m \times n$-matrix. Consider the system of linear equations $A X=b$, which of the following statement is always true: Suppose $m>n$ then rank of augmented matrix $(A \mid b)$ can not larger than $m$. ... solution then $A X=0$ has unique solution. If $A X=b$ has a unique solution then $A$ has to be invertible.

Let $A$ be an $m \times n$-matrix. Consider the system of linear equations $A X=b$, which of the following statement is always true:Suppose $m>n$ then rank of augmented m...

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1.7k views

GO Classes asked Mar 29, 2023

15 votes

3 answers

43

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 26
Given a matrix $A\left(m \times n\right)$ and $A x=b$. Consider below statements : $\text{S}: m<n$ $\mathrm{P}:\; A$ has $m \;\mathrm{Linearly ~Independent}$ columns $\text{R}:$ There is a solution for every $b$ ... $\text{S} \rightarrow \sim \text{P}$ $(S$ and $\text{P}) \rightarrow \text{R}$

Given a matrix $A\left(m \times n\right)$ and $A x=b$. Consider below statements :$\text{S}: m<n$$\mathrm{P}:\; A$ has $m \;\mathrm{Linearly ~Independent}$ columns$\text{...

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1.2k views

GO Classes asked Mar 29, 2023

12 votes

2 answers

44

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 28
Choose the correct statements. If $b>\frac{2}{3}$, then $A=\left[\begin{array}{ll}2 & b \\ 3 & 1\end{array}\right]$ is invertible. If $P$ is an invertible matrix such that $B=P^{-1} A P,$ ... $m$ equations and $n$ variables, such that $m=n,$ always has a solution.

Choose the correct statements.If $b>\frac{2}{3}$, then $A=\left[\begin{array}{ll}2 & b \\ 3 & 1\end{array}\right]$ is invertible.If $P$ is an invertible matrix such that ...

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779 views

GO Classes asked Mar 29, 2023

7 votes

2 answers

45

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 29
Given matrix $A\left(m \times n\right)$ such that $A x=b.$ Consider below statements : $\text{S1}:$ If $b$ is Linearly Dependent on cols of matrix, then it need not always have a unique solution. $\text{S2}:$ If columns of matrix ... $\text{S2}$ is false $\mathrm{S} 2$ is true and $\mathrm{S} 1$ is false

Given matrix $A\left(m \times n\right)$ such that $A x=b.$ Consider below statements :$\text{S1}:$ If $b$ is Linearly Dependent on cols of matrix, then it need not always...

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795 views

GO Classes asked Mar 29, 2023

22 votes

6 answers

46

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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1.5k views

GO Classes asked Mar 14, 2023

1 votes

1 answer

47

DRDO CSE 2022 Paper 1 | Question: 3
With no unique solution, solve for $n$ with the following system of equations $\begin{array}{r} a+b+2 c=3 \\ a+2 b+3 c=4 \\ a+4 b+n c=6 \end{array}$

With no unique solution, solve for $n$ with the following system of equations$$\begin{array}{r}a+b+2 c=3 \\a+2 b+3 c=4 \\a+4 b+n c=6\end{array}$$

admin

286 views

admin asked Dec 15, 2022

3 votes

3 answers

48

Made Easy: Linear Algebra (MSQ)
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ has The trivial solution $X=0$. One independent solution. Two independent solution. Three independent solution.

Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ hasThe trivial solution $X=0$.One independent solution.Two independent solution.Three independent solution.

DebRC

1.1k views

DebRC asked Sep 19, 2022

0 votes

0 answers

49

Best Open Video Playlist for System Of Equations Topic | Quantitative Aptitude
Please list out the best free available video playlist for System Of Equations from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom ... ones are more likely to be selected as best. For the full list of selected videos please see here

Please list out the best free available video playlist for System Of Equations from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then sel...

makhdoom ghaya

186 views

makhdoom ghaya asked Aug 27, 2022

0 votes

0 answers

50

Best Open Video Playlist for System of Linear Equations Topic | Linear Algebra
Please list out the best free available video playlist for System of Linear Equations Topic from Linear Algebra as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO ... ones are more likely to be selected as best. For the full list of selected videos please see here

Please list out the best free available video playlist for System of Linear Equations Topic from Linear Algebra as an answer here (only one playlist per answer). We'll th...

makhdoom ghaya

203 views

makhdoom ghaya asked Aug 14, 2022

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