Write the vectors as a linear combination of ?⃗ 1,2,3 (2, –2, 1), å2= (3, –2, –1) and az = (2, 1,0). Express your answer in terms ofa. Write the vector (-2, 1, –5) as a linear combination of a1the named vectors. Your answer should be in the form 4a1 + 5a2 + 6a3 , which would be entered as 4a1 + 5a2 + 6a3.(-2, 1, –5) =b. Represent the vector (-2, 1, -5) in terms of the ordered basis B = {(2,–2, 1),(3, –2, –1) , (2, 1, 0)}. Your answer should be a vector of thegeneral form <1,2,3>.(-2, 1, -5)]в —

Formula Used : If a vector v can be expressed as a linear combination of a1 →, a2→ , a3→ then there…

a. Write the vector (-2, 1, –5) as a linear combination of āj = (2, –2, 1), ã2 = (3, –2, -1) and az the named vectors. Your answer should be in the form 4āj + 5ã2 + 6a3 , which would be entered as 4a1 + 5a2 + 6a3. (2, 1,0). Express your answer in terms of (-2, 1, –5) = b. Represent the vector (-2, 1,–5) in terms of the ordered basis B = {(2,–2, 1) , (3, –2, –1),(2, 1,0)}. Your answer should be a vector of the general form <1,2,3>. [(-2, 1, —5)]в %3

a. Write the vector (-2, 1, –5) as a linear combination of āj = (2, –2, 1), ã2 = (3, –2, -1) and az the named vectors. Your answer should be in the form 4āj + 5ã2 + 6a3 , which would be entered as 4a1 + 5a2 + 6a3. (2, 1,0). Express your answer in terms of (-2, 1, –5) = b. Represent the vector (-2, 1,–5) in terms of the ordered basis B = {(2,–2, 1) , (3, –2, –1),(2, 1,0)}. Your answer should be a vector of the general form <1,2,3>. [(-2, 1, —5)]в %3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Write the vectors as a linear combination of ?⃗ 1,2,3

(2, –2, 1), å2
= (3, –2, –1) and az = (2, 1,0). Express your answer in terms of
a. Write the vector (-2, 1, –5) as a linear combination of a1
the named vectors. Your answer should be in the form 4a1 + 5a2 + 6a3 , which would be entered as 4a1 + 5a2 + 6a3.
(-2, 1, –5) =
b. Represent the vector (-2, 1, -5) in terms of the ordered basis B = {(2,–2, 1),(3, –2, –1) , (2, 1, 0)}. Your answer should be a vector of the
general form <1,2,3>.
(-2, 1, -5)]в —

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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