Find the dimensions of the following linear spaces The space

Find the dimensions of the following linear spaces. The space of all lower triangular 7 times 7 matrices R^6 times 3 The real linear space C^5

Solution

a)

Lower triangular matrices have all entries above main diagonal equal to 0

So number of entries which can be non zero are: 7 along diagonal and (7^2-7)/2=21

So, total 28 entries

Hence dimension =28

b.

6*3=18

c.

This is a 5 dimensional complex space.

Along each dimension we have a complex number of the form:a+bi ,a and b are both indepdnent

So dimension is:2*5=10