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How to show the polynomials are linearly dependent or independent
How to determine the radius and coordinates of a circle while given equation
Using the row reduction method to solve equations
1/a+bi =c+di
Question 1 of 12 7 Points
What follows is a calculated question with 14 blanks.
If a=⟨ 4,7,8 ⟩ and b=⟨ 5,10,2⟩ then:
|a|= Blank 15. Calculate the answer by read surrounding text.
|b|= Blank 16. Calculate the answer by read surrounding text.
a⋅b= Blank 17. Calculate the answer by read surrounding text.
a×b=⟨ Blank 18. Calculate the answer by read surrounding text.
, Blank 19. Calculate the answer by read surrounding text.
, Blank 20. Calculate the answer by read surrounding text.
⟩
b×a=⟨ Blank 21. Calculate the answer by read surrounding text.
, Blank 22. Calculate the answer by read surrounding text.
, Blank 23. Calculate the answer by read surrounding text.
⟩
a×a=⟨ Blank 24. Calculate the answer by read surrounding text.
, Blank 25. Calculate the answer by read surrounding text.
, Blank 26. Calculate the answer by read surrounding text.
⟩
The angle between a and b is Blank 27. Calculate the answer by read surrounding text.
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
