show all workings please. TIA 1) a) Write down the augmented matrix for the following system...

show all workings please. TIA

1) a) Write down the augmented matrix for the following system of linear equations and solve the system.

3x₁ − 7x₂ + 4x₃ = 10

−x₁ − 2x₂ + 3x₃ = 1

x₁ + x₂ + 2x₃ = 8

b) Jason invested $30 000, splitting it between the three companies Acorn Industries, Balderdash Bank and Chester Challenge. The interest rates were respectively 5%, 6% and 7% per annum. The total annual income (i.e. the sum of the interest payments) was $1700. The income from the investments with Balderdash and Chester was $200 more than the income from the Acorn investment.

Begin by letting the investments with Acorn, Balderdash and Chester be $a, $b and $c respectively

i) Write equations representing three facts about the investments. Discuss your equation as to why it should be this.

ii) Solve this system of equations using an augmented matrix.

iii) How much did Jason invest with each company? Write an answer in words. (Answers to word problems should always be given in words).

Expert Solution

Colby Messinger answered 2 years ago

Write down an augmented matrix in reduced form corresponding to a system with 3 equations and...

Write down an augmented matrix in reduced form corresponding to a system with 3 equations and 5 variables which has infinitely many solutions and 2 free variables. Write down an augmented matrix in reduced form corresponding to a system with 4 equations and 5 variables which has no solutions and 2 free variables.

The following matrix is the augmented matrix for a system of linear equations. A = 1...

The following matrix is the augmented matrix for a system of linear equations. A = 1 1 0 1 1 0 0 1 3 3 0 0 0 1 1 2 2 0 5 5 (a) Write down the linear system of equations whose augmented matrix is A. (b) Find the reduced echelon form of A. (c) In the reduced echelon form of A, mark the pivot positions. (d) Does the system have no solutions, exactly one solution or infinitely...

Write the augmented matrix of the system and use it to solve the system. z. x...

Write the augmented matrix of the system and use it to solve the system. z. x − 2 y − z = − 6 x − y − 2 z = − 4 − x − y + 2 z = − 4

Write the augmented matrix for the following system of linear equations. Solve the equation (x,y,z) by...

Write the augmented matrix for the following system of linear equations. Solve the equation (x,y,z) by row reduction. x+3y-2z=5 3x+5y+6z=7 2x+4y+3z=8

1. For both systems below form the augmented matrix, reduce the augmented matrix to echelon form...

1. For both systems below form the augmented matrix, reduce the augmented matrix to echelon form (zeros below the diagonal), and give the solution to the system. (a) x – 2y + z = 0; 2x + 3y – z = 16; 3x – y – 3z = 23. (b) 2x – 3y + z = -3; x + 2y – 5z = -29; 3x – y + 2z = -2

please show all workings step by step Question 1 M & M Printing is considering the...

please show all workings step by step Question 1 M & M Printing is considering the purchase of a new printing press. The cost of the press is $2 million. This outlay will be partially offset by the sale of an existing press. The old press has zero net book value, cost $1 million ten years ago and can be sold currently for $0.2 million before taxes. As a result of acquiring the new press, sales in each of the...

Give an example of an augmented matrix in echelon form corresponding to a system of 2...

Give an example of an augmented matrix in echelon form corresponding to a system of 2 equations in three unknowns satisfying each of the following conditions or explain why it is not possible. (a) No solutions (b) One unique solution (c) Infinitely many solutions.

(3) Write elimination matrix representing each step in elimination process. ( not augmented matrix) (a) 2x...

(3) Write elimination matrix representing each step in elimination process. ( not augmented matrix) (a) 2x + y − z = 3 x + 3y − z = 6 3x − y + 7z = 8 b) x+y−z−t=0 x + y + 2z − t = 3 2x + 2y + z + 3t = 13 x + 2y + 5z − 7t = 3

1. Use the following information to work Problems (a) and (b). Show all your workings. Michael...

1. Use the following information to work Problems (a) and (b). Show all your workings. Michael is an Internet service provider. On 31 December 2018, he bought an existing business with servers and a building worth $400,000. During his first year of operation, his business grew, and he purchased new servers for $500,000. The market value of some of his older servers fell by $100,000. (a)What was Michael’s gross investment, depreciation, and net investment during 2019? (b)What is the value...

Question 2: Applications of finance (20 Mark) Please answer the following questions. Show all your workings...

Question 2: Applications of finance (20 Mark) Please answer the following questions. Show all your workings when calculations are required and round off your FINAL result to TWO decimal places. You are offered two options by the Waverley Toyota dealer for purchasing a Toyota Landcruiser 4WD. Option 1: Upfront where you pay $100,000 now. Option 2: 2- year monthly payment plan of $4500/month, starting today, with a final payment to be made 23 months from today. a) If the market...

Question