Linear Algebra Answers

Let V={f | f is a polynomial function from the open interval (0,1)={x | 0<x<1} into the set of real numbers, R}, let W={f | f is a function from the open interval (0,1)={x | 0<x<1} into the set of real numbers, R}, and define T:V---->W by the formula T(f)=f'', where the expression

the difference between the circumference and the radius of a circle is 37cm .find its area.

Solve the following system of linear equations by inversion method:
x1 + 6x2 + 4x3 = 2
2x1 + 4x2 - x3 = 3
-x1 + 3x2 + 5x3 =3

express the relationship as a mapping. then determine the domain and range. {(4,9), (6,-4), (-8,1), (10,0), (4,7)}

find the eigenvalue and eigenvector for matrix


0 0 5
S= -2 1 1
3 0 2

Suppose that {v1.....Vn} is a basis for the vector space V. Given any vector v element of V, we can express v as a linear combination v = X1V1+.....+XnVn. The uniqueness of this expression means that mapping v to the n-tuple of coefficients (X1...Xn) defines a function O: V - R^n. Prove that this function is a bijection.

look at matrix

1 -1
Z = 2 4


write matrix Z in its Jordan form ?

look at the matrix
A =
1 2 -2 -1
0 1 2 -3
1 4 2 -7
1 3 0 -4

what is the dimension of the row space of the matrix A ?
what is the dimension of the column space of the matrix A ?
what is the dimension of the null space of the matrix A ?
Give the null space for matrix A ?

look at vectors
1 1 0
u= 0 v= 1 w = 1
1 0 -1

what is the dimension of the space spanned by these three vectors ?

1
is the vector -1 in tyhe span of vectors u , v , and w ?
4