Question

Consider the following matrix. A = 1 k 2 −5 6 1 Assume that the matrix is the augmented matrix of a system of linear equations. (a) Determine the number of equations and the number of variables.

Answer 1

Answer: 2 eqautions and 2 variables

Step-by-step explanation: To solve linear systems, the equations can be represented by an augmented matrix.

To create one, each row represents the coeficients and constants (the numbers after the equal sign) from one equation and each column exhibit all the coeficients for a single variable. This means that the first column of an augmented matrix is for the coeficients of the x-terms, the second for the coeficients of the y-terms, the third column for the z-terms and so on.

For this question:

A = $\left[\begin{array}{ccc}1&k&2\\-5&6&1\end{array}\right]$ or it can be written as

x + ky = 2

-5x + 6y = 1

Thus, the system has 2 equations and 2 variables.