Linear Algebra Answers

Tony purchased a rare 1959 Gibson Les Paul guitar in 2000 for $12,000. Experts estimate that its value appreciates by 14% per year. Write the exponential function then determine its value today (2018).

Mr. Akpalu went to a market to purchase 3 kg of sugar, 10 kg of wheat and 1 kg of salt. In a shop near to Mr. Akpalu’s residence, these commodities are priced at € 20, €10 and € 6 per kg whereas in the local market these commodities are priced at € 15, € 8 and € 6 per kg respectively. If the cost of traveling to local market is € 25, find the net savings of Mr. Akpalu, using matrix multiplication method.

Show that T:R^3 →R^2: T(x,y,z)= (2x+y-z,x+z) is a linear transformation. Verify that T satisfies the Rank-nullity theorem

Express v=(2,-5,3) in R³ as a linear combination of the vectors U₁ =(1,-3,2) , U₂=(2,-4,-1), U₃ =(1,-5,7)

Consider the subspace U of R⁴ spanned by the vectors.

V₁ =(1,1,1,1), V₂= (1,1,2,4 ), V₃= (1,2,-4,-3)

Find

1) an orthogonal bassis of V.

2) an orthogonal basis of V.

Show that the vectors u₁ =(1,1,1), u₂ =(1,2,3), u₃ 3=(1,5,8) span R²

Check whether or not * is a binary operation on S={x∈R| x>0}, where x*y=| In(xy)|

Consider the relation ~ in R^2 given by (x1,X2)~ (y1,y2) if x1x2~y1y2=1. Check if ~ is an equivalence relation

There are at least three unitary matrices of order 2. True or false with full explanation