Question

Q(1) Determine Whether Each Of The Following Systems Is Linear: (A) 3x – 4y + 2yz = 8 (b) ex + 3y = 1(C) 2x-3y+kz=4

Q(2)  Write V As A Linear Combination Of U1, U2, And U3 V=(1,4,6) U1=(1,1,2) U2=(2,3,5) U3=(3,5,8)

Answer 1

1.

Linear systems are systems of equations in which the variables are never multiplied with each other but only with constants and then summed up

a)

not linear: equation has term with variables y, z are multiplied

b)

linear

c)

linear

2.

$v=au_1+bu_2+cu_3$

then:

$a+2b+3c=1$

$a+3b+5c=4$

$2a+5b+8c=6$

if we subtract sum of 1st and 2nd equations from third equation, we get:

$0=1$

so, there are no solutions