Recent questions tagged system-of-equations

Let $m>1$ and $n>1$ be integers. Let $A$ be an $m \times n$ matrix such that for some $m \times 1$ matrix $b_1$, the equation $A x=b_1$ has infinitely many solutions. Let...

The system of linear equations$$\begin{aligned}x-y+2 z & =b_1 \\x+2 y-z & =b_2 \\2 y-2 z & =b_3\end{aligned}$$is inconsistent when ( $b_1, b_2, b_3$ ) equals $(2,2,0)$ $(...

Under which of the scenarios below does the equation $A \vec{x}=\overrightarrow{0}$ have a nontrivial solution. 1. $A$ is a $3 \times 3$ matrix with three pivot positions...

Identify which of the following system of linear equation defined by $A x=b$ are solvable?  $\mathrm{A}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1 \\ 1 & 0\end{array}\right]$ ...

When does a system of linear equations $A x=b$ have no solution?when $\operatorname{Rank}(A)<\operatorname{Rank}([A \mid b])$when $\operatorname{Rank}(A)=\operatorname{Ra...

If $A$ is an $m \times 5$ matrix and $A \vec{x}=0$ has a unique solution, then which of the following is true. Select only one.A. $m \geq 5$B. $m=5$C. $m \leq 5$D. $m$ ca...

$\begin{equation}\begin{aligned}&\text{Given a matrix } \boldsymbol{P} =\begin{bmatrix}1 & 2 & 3 \\2 & 1 & 2 \\3 & 3 & 5\end{bmatrix}\text{ and a vector } \boldsymbol{b} ...

If $A x=0$ has some nontrivial solution then columns of $A$ are linearly dependent ? (Please enter $1$ for $True$ and $0$ for $False$)

​​​​​The sum of the elements in each row of $A \in \mathbb{R}^{n \times n}$ is 1. If $B=A^{3}-2 A^{2}+A$, which one of the following statements is correct (for $x \in \ma...

Consider a system of linear equations $P X=Q$ where $P \in \mathbb{R}^{3 \times 3}$ and $\mathrm{Q} \in \mathbb{R}^{3 \times 1}$. Suppose $P$ has an LU decomposition, $P=...

Consider the given system of linear equations for variables $x$ and $y$, where $k$ is a real-valued constant. Which of the following option(s) is/are CORRECT?$$ \begin{ar...

If given b is a linear combination and since rank =5 all the columns are linearly indepndent then why would this statement be false

Find values of $x$ and $y$ that satisfy both the following equations:\[\begin{aligned}\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}} & =\frac{5}{2} \\\frac{x}{\sqrt{y}}+\frac{y}{\...

Consider the system of linear equations: $x+y+z=5, \quad 2 x+2 y+3 z=4$. Thenthe system is inconsistentthe system has a unique solutionthe system has infinitely many solu...

For the system of linear equation Ax=0 where matrix A(mxn) , what can we say about the number of solutions for this equation :1. if all n columns of A are linearly Indepe...