Linear Algebra Answers

Let U and V be vector spaces over a field F. Let T:U→V is one-one if and only if ...

(A) rank (T) = 0
(B) rank (T) = 1
(C) Ker (T) = 0
(D) Ker(T) = 1

Let U and V be vector spaces over a field F and dim U = n. Let T:U→V
be a linear operator, then rank (T) + nullity (T) = ...

(A) 0
(B) 1
(C) n-1
(D) n

Let U and V be vector spaces over a field F,a function T:U→V
such that
T(u1+u2)=T(u1)+T(u2), for u1,u2∈U and T(αu)=αT(u) for α∈F and u∈U
is called a ………….

(A) Vector space
(B) Transformation
(C) Linear transformation
(D) Nullity

\begin{bmatrix}1&2&4\\2&5&3\\4&3&8\end{bmatrix}

is a ...... Matrix

(A) Symmetric
(B) Asymmetric
(C) Square
(D) Skew-symmetric

The determinant of

\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}

is....

(A) 0
(B) 1
(C) 2
(D) 3

A Matrix is a .....

(A) Square array of numbers arranged in rows and columns.
(B) Rectangular array of numbers arranged in rows and columns.
(C) Triangular array of numbers arranged in rows and columns.
(D) Circular array of numbers arranged in rows and columns.

Use Branch and Bound technique to solve the following problem Maximise z = 3x1 + 3x2 + 13 x3 Subject to – 3x1 + 6x2 + 7x3 ≤ 8 6x1 – 3x2 + 7x3 ≤ 8 0 ≤ xj ≤ 5 And xj are integer j = 1, 2, 3. (Operation Research)

1. Solve the following simultaneous equations by using Cramer’s rule

3x+2y=13
2x-y=4

Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Solve for a and b