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Recent questions tagged system-of-equations
7
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GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 49
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$ no solutions for some but not all $\vec{p}$; exactly one solution for all other $\vec{p}$ exactly one solution for ... some $\vec{p}$, exactly one solution for some $\vec{p}$ and more than one solution for some $\vec{p}$
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$no solutions for some but not all $\vec{p}$; exactly one sol...
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Linear Algebra
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Memory Based GATE DA 2024 | Question: 53
Consider the following scenarios involving linear algebra: For a \(3 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution? For a \(3 \times 3\) matrix, if some vector p ... 2 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution?
Consider the following scenarios involving linear algebra:For a \(3 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an in...
GO Classes
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Feb 4
Linear Algebra
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5
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GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 36
Consider the system $A \mathbf{x}=\mathbf{b}$, with coefficient matrix $A$ and augmented matrix $[A \mid b]$. The sizes of $\mathbf{b}, A$, and $[A \mid \mathbf{b}]$ are $m \times 1, m \times n$ ... $\operatorname{rank}[A]>$ $\operatorname{rank}[A \mid b]$.
Consider the system $A \mathbf{x}=\mathbf{b}$, with coefficient matrix $A$ and augmented matrix $[A \mid b]$. The sizes of $\mathbf{b}, A$, and $[A \mid \mathbf{b}]$ are ...
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Jan 13
Linear Algebra
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Possible Solutions for a System of Linear Equations
Consider a matrix of dimensions mxn and if rank(A)=n. What can be infer about the possible solutions?
Consider a matrix of dimensions mxn and if rank(A)=n. What can be infer about the possible solutions?
Sriram M
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Sriram M
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Jul 3, 2023
Linear Algebra
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9
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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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Apr 5, 2023
Linear Algebra
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14
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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...
GO Classes
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Apr 5, 2023
Linear Algebra
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16
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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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Apr 5, 2023
Linear Algebra
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10
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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...
GO Classes
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GO Classes
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Mar 29, 2023
Linear Algebra
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13
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3
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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 ...
GO Classes
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GO Classes
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Mar 29, 2023
Linear Algebra
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10
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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...
GO Classes
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GO Classes
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Mar 29, 2023
Linear Algebra
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8
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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...
GO Classes
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GO Classes
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Mar 29, 2023
Linear Algebra
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7
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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...
GO Classes
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GO Classes
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Mar 29, 2023
Linear Algebra
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8
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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 ...
GO Classes
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GO Classes
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Mar 29, 2023
Linear Algebra
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