Let u = 2i + j, v = i + j, and w = i - j. Find scalars a and b such that u= av + bw.

A complex number is of the form where are real numbers.

So,

Therefore,

Add these equations.

So,

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Step-by-step explanation:

Given the expression u= av + bw where u = 2i + j, v = i + j, and w = i - j, to find the scalars a and b, we will first substitute the vectors into the expression given as shown;

u= av + bw

2i + j = a( i + j)+b(i-j)

open the parenthesis

2i + j = ai+aj+bi-bj

collect like terms at the right hand side of the equation

2i + j = ai+bi+aj-bj

2i + j = (a+b)i+(a-b)j

compare the coefficient of complex value i and j on both sides

a+b = 2 1

a-b = 1 2

solve the resulting equation simultaneously using elimination method

Subtract both equation from each other.

(a-a) +(b-(-b))= 2-1

0+2b = 1

b = 1/2

Substitue b = 1/2 into equation 2 to get a

From equation 2, a = 1+b

a = 1 + 1/2

b = 3/2

Hence the scalars a and b are 1/2 and 3/2 respectively

square root

step-by-step explanation: