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Sagot :
The vector space of 2×2 matrices under addition over a field F is 4 dimensional. It's span{(1000),(0100),(0010),(0001)}. These are clearly independent under addition.
Given,
The set of 2 x 2 matrices is a linear space (zero matrix exists, multiplication by a scalar is well defined, the sum of two matrices is a matrix, etc.)
Now, According to the question:
How do you define a 2x2 matrix?
A 2⇥2 matrix (pronounced “2-by-2 matrix”) is a square block of 4 numbers. is a 2 ⇥ 2 matrix. It's called a 2 ⇥ 2 matrix because it has 2 rows and 2 columns. The four numbers in a 2 ⇥ 2 matrix are called the entries of the matrix.
What is the dimension of the 2 x 2 matrices?
The vector space of 2×2 matrices under addition over a field F is 4 dimensional. It's span{(1000),(0100),(0010),(0001)}. These are clearly independent under addition.
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