Linear Algebra Answers

Investigate the linear dependence and independence of the vector X1=(1,2,3), X2=(2,-1,3), X3=(0,1,2), X4=(-3,7,2)

Use matrix method to solve d^2x/dx^2+4x+2=0, x(0)=1 , x(0))=0

R^3 is a inner product space over the inner product

<(x1,x2,X3),(y1,y2,y3)> = x1y1+ x2y2 - x3y3

True or false with full explanation

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