Search & Filtering
suppose v are finite dimensional of t € l(v,w). show that with respect to each of bases of v and w, the matrix of t has at least dim range t nonzero entries
Assume that U is a plane. Find out whether or not the following vectors lie in U:
(10.1) ~u =< 3.8, 1 >, ~v =< −4, 1, 1 > and w~ = −~v
(10.2) ~u =< 3.8, 1 >, ~v =< −4, 1, 1 > and w~ = ~u − ~v
Example of Vector space and subspace in which it's all properties must satisfied.
2 Let A [ 1 𝑖 −𝑖 2 ] And let g be the form (on the space of 2x1 complex matrices) defined by g(X,Y) =Y*AX.Is g an inner product ?
What do you mean by positive form, negative form? Define these with example ( inner product space)
determine if set of vectors are linearly independent v1={4,1,2}, v2={-3,0,1} and v3={1,2,1}
Inspect the following without finding the determinant:
1.
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 - 2]
2. [1 0 0 0]
[0 1 0 0]
[0 0 0 1]
[0 0 1/4 0]
Show that if A is a matrix with a row of zeros,then A cannot have an inverse
Using the the concept of rank of the matrix find whether the following system of equations
are consistent or inconsistent,
i.
4y + z = 0
12x - 5y - 3z = 34
-6x + 4z = 8
ii.
5x - 3y + z = 7
2x + 3y - z = 0
8x + 9y - 3z = 2:
iii.
-8x + 2z = 1
6y + 4z = 3
12x + 2y = 2
Using the the concept of rank of the matrix find whether the following system of equations
are consistent or inconsistent,
i.
4y + z = 0
12x - 5y - 3z = 34
-6x + 4z = 8
ii.
5x - 3y + z = 7
2x + 3y - z = 0
8x + 9y - 3z = 2:
iii.
-8x + 2z = 1
6y + 4z = 3
12x + 2y = 2
