Linear Algebra Answers

Balance the given chemical equation using linear equations (gussis Jordan elimination method).

Na₂CO3 + C + N₂ ---> NaCN + CO

Consider the linear equation 2a + 3b = 4

Is (a; b) = (1; 1

2

) a solution to the equation? Motivate your answer.

10 Look up the concept of a homogeneous linear system.

Which of the following linear systems is homogeneous. [just give the answer I) or II) or III) : no motivation

is required.]

I) 3x + 14y = 0 & 2x − 3y = 7

II) 7x + 2y = 10 & 11x − 0y = 7

III) 4x − 23y = 0 & 7x − 3y = 0

11.) You have a linear homogeneous system in three variables. Give a solution that this system must have.

T

) East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided. What is the center of gravity?

X-coordinate

Y-coordinate

Volume

Athens, Texas

30

30

150

Beaumont, Texas

20

10

350

Carthage, Texas

10

70

100

Denton, Texas

50

50

200

Find the real root of the equation 𝑥𝑒𝑥=2 correct upto two decimal places using the method of false position.

2.8. Let P be the property “is a prime number” and O be the property “is an odd

integer.” Consider the sets A = {x ∈ N : P(x)} and B = {x ∈ N : O(x)}.

1. Examine A and B with respect to the subset relation. What can you conclude? Justify your

answer.

2. Are A and B equal? Justify your answer.

9.) Look up what is meant by a system of linear equations.

A known fact of solutions of systems of linear equations is that only one the following options can hold :

(i) No solution possible

(ii) A unique solution can be found

(iii) The system has infinite solutions.

Consider that two straight lines form a linear system.

Interpret what happens geometrically to the straight lines to get each case of the solution types given

abo

Which of the following linear systems is homogeneous. [just give the answer I) or II) or III) : no motivation

is required.]

I) 3x + 14y = 0 & 2x − 3y = 7

II) 7x + 2y = 10 & 11x − 0y = 7

III) 4x − 23y = 0 & 7x − 3y = 0

Let X =

1 2

3 4

; E =

a

b



Find each of the following.

If the operation cannot be done : state undefined operation.

a) XE

b) EX

c) XT X where XT

stands for the transpose of X

Consider the linear equation 2a + 3b = 4

Is (a; b) = (1; 1

2

) a solution to the equation? Motivate your answer.