a) Determine a basis of M mxn(R). Justify your result, i.e show that your collection of vectors is in fact linearly independent and spans Mmxn(R). What is the dimension of Mmxn(R)?
b) Show that in the case of square matrixes (m=n) the subset of symmetric matrices Snxn(R) is a subspace of M nxn (R). What is the dimension of M mxn(R)?
c) P 3 (R) <= 3 degree, show that x^3 + 2x^2 , x^2 + x and x^3+3x are linearly independent?
Can someone help me with these questions?
b) Show that in the case of square matrixes (m=n) the subset of symmetric matrices Snxn(R) is a subspace of M nxn (R). What is the dimension of M mxn(R)?
c) P 3 (R) <= 3 degree, show that x^3 + 2x^2 , x^2 + x and x^3+3x are linearly independent?
Can someone help me with these questions?