Linear Algebra Answers

Using matrix method, solve the simultaneous equations {x-3y=3

5x-9y=11

Michael is a bicycle commuter. he has observed that the reduces the time for his 9 km commute by 15 min when he increases his average speed by 3 km/h. what is Michael's faster speed?

Employ the Gauss-Seidel method, solve the system. 10𝑥 + 𝑦 + 𝑧 = 12 2𝑥 + 2𝑦 + 10𝑧 = 14 2𝑥 + 10𝑦 + 𝑧 = 13

Determine all eigenvalues and the corresponding eigenspaces for the matrix 𝐴 = [ −9 4 4 −8 3 4 −16 8 7 ]

Let the vector space V=R^3 and W={(a,b,c);a+b+c=0} i.e. W consists of those vectors each with the property that the sum of its components is zero. Is W a subspace of V

B1 and B2 are two types of boats which are to be used to ferry 800 troops and 90 tons of equipment across a lake. Each B1 can carry 200 men and 15 tons of equipment while each B2 can carry 100 men and 15 tons of equipment. If each B1 costs Rs. 90 to operate and each B2 costs Rs. 44 to operate, find the number of each boat that should be used if the cost is to be minimum.

Give a geometric description of a single linear equation in three variables. Then give a geometric description of the solution set of a system of 3 linear equations in 3 variables if the system

(a) is inconsistent.

(b) is consistent and has no free variables.

(c) is consistent and has exactly one free variable.

(d) is consistent and has two free variables

Find the standard matrix A for the linearly transformation T :R^2_R^2

5)Solve the following linear programming problem using two phase method. 

Minimize z = -3x1 + x2 - 2x3 

Subject to 

x1 +3x2 +x3 ≤5 

2x1 –x2 +x3 ≥2 

4x1 + 3x2 - 2x3 = 5 

x1, x2, x3 ≥ 0