infinite solutions

Consider the system of linear equations given below. $$ \begin{aligned} a x+y & =b \\ 16 x+a y & =24 \end{aligned} $$ Suppose the values of a and b are chosen such that the system...

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? x + ky = 1 kx + y = -1

Consider the given system of linear equations for variables $x$ and $y$, where $k$ is a realvalued constant. Which of the following option(s) is/are CORRECT? $$\begin{aligned} & x+...

Let $${c_1},.....,\,\,{c_n}$$ be scalars, not all zero, such that $$\sum\limits_{i = 1}^n {{c_i}{a_i} = 0} $$ where $${{a_i}}$$ are column vectors in $${R^{11}}.$$ Consider the set...

Consider the following system of linear equations $$$\left[ {\matrix{ 2 & 1 & { - 4} \cr 4 & 3 & { - 12} \cr 1 & 2 & { - 8} \cr } } \right]\left[ {\matrix{ x \cr y \cr z \cr } } \r...