[Math] Which of the following statements about Matrix A are NOT TRUE

linear algebramatrices

A = {(1 2 -6 0),(0 1 4 -1),(0 0 1 -3),(0 0 0 1)}

1) Rank of A is 4

2) Columns of A span R4

3) Rows of A are linearly independent

4) A is invertible

my logic was that the Rank is 4 because the matrix has 4 leading 1's, and the column space is in R4 for the same reason. The rows are linearly independent because it is in Row-Echelon form. And i was able to invert the matrix and confirm it with excel.

I think its the column span but i am not entirely sure.

Any help correcting my thinking would be very appreciated.

This is a homework question just in case it matters.

Best Answer

All four statements are equivalent (I'm guessing you can find it with several different theorems of your lesson), and they are all true. Proving one of them is true is enough. Personally, since you have an "upper triangle" matrix I would go with this :

https://en.wikipedia.org/wiki/Determinant#Properties_of_the_determinant

Related Question