Question 1 (5 points): Consider the system of linear equations x1 − 4x2 − x4 = −7 x2 − 2x4 = 3 x4 + 2x5 = 3 (a) Write down the coefficient matrix of this system. (b) Write down the augmented matrix of this system. (c) Use row operations to put the augmented matrix into reduced echelon form. Make it clear which row operations you are using. (d) Is the system consistent or inconsistent? Explain your answer. (e) If the system is consistent, use your answer to part (c) to find the solution to the linear system.

Step-by-step explanation:

Given is a system of equations as

We have 5 variables and 3 equations

a) coefficient matrix of this system is

1   -4   0   -1   0\\

0    1   0   -2   0\\

0    0   0    1    2\\

We find that x3 has no coefficient in any of the equations so we can omit x3 and write as equations for 4 variables as

1   -4     -1   0\\

0    1     -2   0\\

0    0     1    2\\

b) Augmented matrix is

1   -4     -1   0\\  7

0    1     -2   0\\ 3

0    0     1    2\\3

c) For row operations to ehelon form

we can do R1+4R2 = R1

We get

1   0   -9  0 \\  19

0   1  -2   0 \\   3

0   0   1   2  \\   3

Now let us do R1 = R1+9R3 and R2 = R2+2R3

1  0   0   0  \\ 46

0  1   0   0   \\  9

0   0  1   2   \\  3

d) We find that there are infinite solutions to  the system in parametric form, since x4 and x5 are linked with only one equation

e) x1 = 46, x2 = 9, x4+2x5 =3

Or x1 =46, x2 =9, x4 = 3-2x5, x5 = x5 is the parametric solution

at first, in 1635, the evening meetings had been just for women . .

what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500