its definiely true: eigenvalues don't change under row operations. If you have a diagonal matrix, you can check the entries are eigenvalues by pairing them with standard basis vectors as the eigen vectors.
4 rows and 6 columns: Like hypnotik said: a matrix of all zeros has rank 0 due to all 4 rows being 0 and has nullity 6 due to all columns being zero.
The zero matrix will be the only matrix that satisfies this condition. If you have one nonzero entry the rank becomes 1 and nullity becomes 5.
Just define the function piece-wise using the greatest integer function |_x_|:
Let f(x)=x-|_x_| if |_x_| is even
and
f(x) = 1-x+|_x_| if |_x_| is odd
This fucntion will just be the lines y=x and y=1-x on [0,1] repeated over and over.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.