Invertible Matrix over Complex Numbers

Let A be a square n x n matrix over C[X] and write A = [pjk (X)] . For any z∈C( z being a complex variable) let A(z) := [pj k (z)] , that is a square n x n matrix over C. Show that matrix A is invertible if and only if matrix A(z) is invertible for all z from C. Will it be still valid if we change complex numbers into ...continues

Linear Algebra Linear Dependence of Vector Spaces

Question : Prove that ( 1 , 3 , 2 ) , ( 1 , – 7 , – 8 ) , ( 2 , 1 , – 1 ) of V3( R) is linearly independent.

Linear Programming : Optimal Solution

Max Z = 5x1 + 6x2 s.t. 17x1 + 8x2 < = 136 3x1 + 4x2 < = 36 x1, x2 > = 0 What is the optimal solution? Z = ?

Finding Basis and Dimension of the Subspace generated by given vectors. For complete description of the specific problems please see the problems.

Question (1) Find a basis and dimension of the subspace W of R4 generated by the vectors ( 1 , – 4 , – 2 , 1 ) , ( 1 , – 3 , – 1 , 2 ) , ( 3 , – 8 , – 2 , 7 ) . Extend it to find the basis of R4 . Question (2) Determine a basis and the dimensions of the Subspace of M2(R) generated by the 2 by 2 Matrices [ 2 -10 ] , [ ...continues

Finding Basis and Dimension of the Subspace generated by given vectors. For complete description of the specific problems please see the problems.

Question (1) Find a basis and dimension of the subspace W of R4 generated by the vectors ( 1 , – 4 , – 2 , 1 ) , ( 1 , – 3 , – 1 , 2 ) , ( 3 , – 8 , – 2 , 7 ) . Extend it to find the basis of R4 Question (2) Determine a basis and the dimensions of the Subspace of M2(R) generated by the 2 by 2 Matrices [ 2 -10 ] , [ ...continues

Linear Operators Solving Equations Finding Annihilator of a Space

Question (4) Solve the equations over R X1 + 2X2 – 3X3 + 4X4 = 0 X1 + 3X2 – X3 = 0 6X1 + X3 + 2X4 = 0 Question(5) If F = R find Annihilator A(W) of the space W spanned by (2 , 4 , 6 ) , ( 1 , 6 , 2 ). ( Note : Here F is the field and R represents the set of Real Numbers) See attached file for full problem desc ...continues

Finding Annihilator and solving matrix equations by reducing them to Echelon form is explained in detail. For specific problem description, please see the problems.

Question (4) Solve the equations over R X1 + 2X2 – 3X3 + 4X4 = 0 X1 + 3X2 – X3 = 0 6X1 + X3 + 2X4 = 0 Question(5) If F = R find Annihilator A(W) of the space W spanned by (2 , 4 , 6 ) , ( 1 , 6 , 2 ). ( Note : Here F is the field and R represents the set of Real Numbers) For the description of the questi ...continues

Linear Operator Finding Basis and Dimension of Range and Kernel For complete description of the problems, please see the questions.

Question (1): Let T: R^3 into R^3 be a linear transformation defined by T(x, y, z) = (x + 2y – z, y + z, x + y – 2z ) Find a basis and the dimension of ( i ) Range of T ( ii) the Kernel of T Question (2) : If T:R^4 into R^3 is a linear transformation defined by T( a, b, c, d) = ( a – b + c + d, a + 2c – d, ...continues

The answer should look like this x12 + x34 = 500, with the correct numbers filled in.

In setting up the an intermediate (transshipment) node constraint, assume that there are three sources, two intermediate nodes, and two destinations, and travel is possible between all sources and the intermediate nodes and between all intermediate nodes and all destinations for a given transshipment problem. in addition, assume ...continues

What are the total monthly transportation costs for the optimal solution?

A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are: Destination Assembly Plant 1 2 3 Supply Source A 5 9 16 200 Factory B 1 2 6 400 C 2 8 7 200 Demand 120 620 60 What are the total monthly tr ...continues