Chapter 1 - Systems of Linear Equations - 1.2 Gaussian Elimination and Gauss-Jordan Elimination - 1.2 Exercises - Page 24: 55

(a) The unit matrix $I_2$, that is $$I_2=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right].$$ (b) The matrices on the form $$\left[\begin{array}{ll}{1} & {a} \\ {0} & {0}\end{array}\right], \quad a\in R.$$ For example, the matrix $$\left[\begin{array}{ll}{1} & {3} \\ {0} & {0}\end{array}\right].$$

Work Step by Step

The possible $2\times 2$ reduced row-echelon matrices can be one of the following forms: (a) The unit matrix $I_2$, that is $$I_2=\left[\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right].$$ (b) The matrices on the form $$\left[\begin{array}{ll}{1} & {a} \\ {0} & {0}\end{array}\right], \quad a\in R.$$ For example, the matrix $$\left[\begin{array}{ll}{1} & {3} \\ {0} & {0}\end{array}\right].$$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.