Answer to Question #137495 in Linear Algebra for Sarita bartwal

Question

The coefficient matrix of any linear system must be square matrix.
True or false with correct explanation

Answer 1

It's false.

In general, a system with m linear and n unknowns can be written as

$a_{11}x_1 + a_{12}x_2 + ... + a_{1n}x_{n} = b_1$

$a_{21}x_1 + a_{22}x_2 + ... + a_{2n}x_{n} = b_2$

$\vdots$

$a_{m1}x_1 + a_{m2}x_2 + ... + a_{mn}x_{n} = b_m$

where $x_1, x_2 ...x_n$ are the unknowns and the numbers $a_{11}, a_{12}, ... a_{mn}$ are the coefficients of the system. So, the coefficient matrix is the mxn matrix with the coefficient $\displaystyle a_{ij}$ as the (i,j)-th entry:

$\begin{pmatrix} a_{11} & a_{12} \space \space \space \dots & a_{1n}\\ a_{21} & a_{22} \space \space \space \dots & a_{2n}\\ &\vdots\\ a_{m1} & a_{m2} \space \space \space \dots & a_{mn}\\ \end{pmatrix}$