What is the rank of M = [1 2 3 4; 2 4 6 8; 1 0 1 0]?

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Rank of a wide matrix

Linear algebraEasy

What is the rank of $M = 121240361480$ ?

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Hint

Look for a row that is a multiple of another.

Solution

Row $2$ is exactly $2$ times row $1$ , so it adds nothing to the row space.
Rows $1$ and $3$ are not multiples of each other, since row $3$ has a $0$ where row $1$ has a $2$ .
So the row space has dimension $2$ , and the rank of $M$ is $2$ .

Answer: $2$