Linear Algebra Answers

write vector v=(4,9,19) as a linear combination of vectors u1=(1,-2,3),u2=(3,-7,10),u3=(2,1,9)

Given               B 2 31 2 21 1 32 find the eigenvalues of B and an eigenvector for B corresponding to  1.

Use simplex method to maximize 𝑓=3𝑥+5𝑦+4𝑧

subject to the conditions

2𝑥+3𝑦≤18

2𝑥+5𝑦≤10

3𝑥+2𝑦+4𝑧≤15

and 𝑥,𝑦,𝑧 ≥0.

Consider the function y=tan(x)

(a) Show that the first two non-zero terms in the Maclaurin series of y are x+1/3x³...

(b) Use the first two terms of the Maclaurin series of y to estimate tan (1/3).

Reduce the quadratic form

2 2 2 8 7 3 12 – 8 4 x y z xy yz zx    

to the canonical form

through an orthogonal transformation and hence show that it

is positive Semi-definite.

1. The figure shows two bases, consisting of unit vectors, for ll?2: S —— (i,j) and 0 = (ut,ut).

(a) Find the transition matrix s B

(b) Find the transition matrix PB S

1.   The figure shows two bases, consisting of unit vectors, for ll?²: S —— (i,j) and 0 = (ut,ut).

(a)    Find the transition matrix  s B

(b)    Find the transition matrix PB S

Employ the Gauss-Seidel method, solve the system.

10𝑥 + 𝑦 + 𝑧 = 12

2𝑥 + 2𝑦 + 10𝑧 = 14

2𝑥 + 10𝑦 + 𝑧 = 13