1. ## Finding the vector

The set M(2,2) of a 2x2 matrix, with real entries, is a vector space.

The set of diagonal matrices
D=(a 0 )
( 0 b )

where a, b are real numbers. is a subset of M(2,2).

i)

Write down two particular matrices which belong to
D, and two particular matrices which belong to M(2,2) but not D.

Two matrices which belong to D are

(a) (0)
v =(0) u=(b)

I don't get the other part.. which does not belong to D.

2. Originally Posted by Khonics89
The set M(2,2) of a 2x2 matrix, with real entries, is a vector space.

The set of diagonal matrices
D=(a 0 )
( 0 b )

where a, b are real numbers. is a subset of M(2,2).

i)

Write down two particular matrices which belong to
D, and two particular matrices which belong to M(2,2) but not D.

Two matrices which belong to D are

(a) (0)
v =(0) u=(b)

I don't get the other part.. which does not belong to D.
Is $I_2\in D$?

3. It does not specify!