Question 3
25 pts
The matrix
\[
\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 2 \\
0 & 0 & 0
\end{array}\right]
\]
is in reduced form.
True
False

Step 1 ：The given matrix is \[\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]\]

Step 2 ：The statement is 'The matrix is in reduced form'.

Step 3 ：Reduced form of a matrix means that it is in row echelon form and every leading coefficient is 1 and is the only non-zero entry in its column.

Step 4 ：In the given matrix, the second row has a leading coefficient of 1, but there is another non-zero entry in its column. Therefore, the matrix is not in reduced form.

Step 5 ：So, the statement 'The matrix is in reduced form' is False.

Step 6 ：Final Answer: The statement 'The matrix is in reduced form' is \(\boxed{\text{False}}\)