Consider the set $$H$$ of all $$3$$ $$X$$ $$3$$ matrices of the type $$$\left[ {\matrix{ a & f & e \cr 0 & b & d \cr 0 & 0 & c \cr } } \right]$$$

Where $$a, b, c, d, e$$ and $$f$$ are real numbers and $$abc$$ $$ \ne \,\,0$$. Under the matrix multiplication operation, the set $$H$$ is:

What are the eigen values of the following $$2x2$$ matrix? $$$\left[ {\matrix{ 2 & { - 1} \cr { - 4} & 5 \cr } } \right]$$$

In an M$$ \times $$N matrix such that all non-zero entries are covered in $$a$$ rows and $$b$$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is

How many solutions does the following system of linear equations have?

- x + 5y = - 1
x - y = 2
x + 3y = 3