Linear Algebra Answers

let B={1-t,t-t²,2-2t+t²} be an ordered basis for p₂

let p(t)=3+t-6t²

1. find [p(t)]_B

1.Which of the following is the solution of the equation below?

0x + 0y = 0

1. (0,0,0).

2. (1,0,0).

3. No such solution exists

4. Infinitely many solution or (-1,2,1).

A, B and C are on a betting game. B loses Php 350 of his money to A. As a result, A now has twice as much as what is left with B. Then, C loses Php 700 to B. As a consequence, C now has only one-third as much money as B would then have. If A has loses Php 210 to C, C will have as much as money as A would have left. How much did each have at the start?

Consider A = <0,4,2> , B = <6,-1,0> , and C = <3,0,1>. Find scalars a, b and c such that aA + bB = (c - 1)C.

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1.1 Prove that the characteristic polynomial of a 2 × 2 matrix A can be expressed as

λ^2 − tr(A)λ + det(A), where tr(A) is the trace of A.

In Exercises 15–16, determine whether the expression makes sense mathematically. If not, explain why?

15. (a) u · (v · w)

(b) u · (v + w)

(c) u · v

(d) (u · v) − u 

 Suppose that a vector a in the xy-plane points in a direction that is 47◦ counterclockwise from the positive x-axis, and a vector b in that plane points in a direction that is 43◦ clockwise from the positive x-axis. What can you say about the value of a · b?

Define W =  x y  : xy ≥ 0  . Decide if V is a vector space or notand prove your claim. (Hint: V is the union of the first and third quadrants in the xyplane)