Linear Algebra Answers

For any two subspace W1,W2 of R^3 of dimension 2, W1+ W2 is a direct sum . True or false with full explanation

Show that a field f may be considered as a vector space over f if scalar multiplication is identified with field multiplication

Prove that the set of all vectors in a plane over the field of real numbers is a vector space

Let V be a vector space over a filed F and x,y,z is an element of V then show that the set of all liner combinations of x,y and z,W=(ax+by+cz:a,b,c are an element of F) is a subspace of V over F. This subspace is called the span of (x,y,z)

Give an example showing that the union of two subspace of a vector space V over a filed F is not necessarily a subspace of V over F.

if | A| = -7 find x where A ( 3 X 2 1)

Complete { (2, 0, 3)} to form an orthonormal basis of R^3

Complete { (2, 0, 3)} to form an orthogonal

basis of R³

Given that A= 3 ‐1 2 and B= 4 [‐1 2]

[5 1 7] 5 1 3

I. Evaluate 3A and 2B

ii. 3A‐2B

Given that C= 1 6

[3 9]

4 -3 Evaluate CB

Reduce 2++x²+2x₂x4x−2x4, into canonical form. Find the rank,

index, signature and its nature.