Question

In Exercises 23-26, describe the possible echelon forms of the matrix. Use the notation of Example 1 in Section 1.2

25. \(A\) is a \(4 \times 2\) matrix, \(A = \left[ {\begin{array}{*{20}{c}}{{a_1}}&{{a_2}}\end{array}} \right]\) and \({a_2}\) is not a multiple of \({a_1}\).

Short answer

The echelon form of the \(4 \times 2\) matrix is ,.

Step-by-step solution

Recall the notation of example 1 used for matrices in the echelon form

In example 1, the following matrices are in echelon form. The leading entries may have any non-zero value, and the starred entries \(\left( * \right)\) may have any value (including zero).

Use the above notation to determine the echelon forms of the matrix

It is given that \(A\) is a \(4 \times 2\) matrix, \(A = \left[ {\begin{array}{*{20}{c}}{{a_1}}&{{a_2}}\end{array}} \right]\), and \({a_2}\) is not a multiple of \({a_1}\).

Use the leading entries and starred entries \(\left( * \right)\) to construct the echelon form of the \(4 \times 2\) matrix.

,

Thus, the echelon form of the \(4 \times 2\) matrix is ,.