Linear Algebra Answers

AN ALTITUDE OF A TRIANGLE IS 5/3 THE LENGTH OF ITS CORRESPONDING BASE. IF THE ALTITUDE IS INCREASED BY 4CM AND THE BASE DECREASEDBY2CM,THE AREA OF THE TRIANGLE REMAIN THE SAME .FIND THE BASE AND THE ALTITUDE OF THE TRIANGLE

A linear tansformation T:U→F is a called a ........ if
T(α1u1+α2u2)=α1T(u1)+α2T(u2), for α1α2∈F and u1u2∈U.

(A) linear dimensional
(B) linear function
(C) linear functional
(D) linear dimension

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

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

In V3(R), Find dim(A+B) and dim(A^B) where A is the subspace spanned by (1,1,1) and B is the subspace spanned by (-1,-1,-1).