Question

Determine the dimension of the vector space. M4,2

STEP 1: Determine the number of linearly independent vectors needed to span M4,2. The basis for M4,2 has linearly independent vectors.
STEP 2: Using the result from Step 1, determine the dimension of M4,2.

Answer 1

STEP 1

M_{4,2} is set of 4x2 matrices hence each matrix has 4*2=8 entries. Each entry can be filled independently.

Hence its basis has 8 linearly independent vectors.

STEP 2

Dimension= cardinality of basis = 8.