Suppose that A = and B = for some real numbers x and y. Find y 1 9 y all ordered pairs (r, y) such that AB = BA. (Enter your answer as a list of ordered pairs; for example, (1,2), (3,4), (5,6) .) Answer: (0,3),(0,-3),(0,9),(1,0).

Q: Show that z*dz 0 for any integer k + 1 where C is given by y(0) Reio for 0 < 0 < 27. (7a) by showing…

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Q: f = {(-9, – 2), (-8, 5), (-6, 1), (- 3, 7), (–1, – 2),(0, – 10)} and g = {(-7,7), (-6, 6), (-5, 5),…

A: Given that, f = {(-9, -2), (-8, 5), (-6, 1), (-3, 7), (-1, -2), (0, -10)} g = {(-7, 7), (-6, 6),…

Q: 4x+2y=2 1.) 2x+2y=4

A: The given system of equation is: 4x+2y=22x+2y=4

Q: Let a = (-5, 5, 4) and 6 = (-1,-4, 5). (a) a × b x (41,-21,24) x (b) b × ā X = (c) (ã × b) × ã = (d)…

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Q: Let à = (2, 3, 4) and b = ( − 2, 0, — 5). Find à x 6.

A: A detailed solution is given below

Q: A researcher measures the relationship between education (in years) and investment gains (in…

A: We have given that data  And i want to find  Correlation coefficients ( r )

Q: What is the equation of the line perpendicular to 2x − 3y + 5 = 0 and passes through - point of…

A: Please refer to the image below

Q: If a = [1, 2]  and  b = [2, 7], find a + 2b.

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Q: x+y 1 16 and If bg-, 8 = -3 calculate the values of x and y.

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Q: Do the points (1, 5, −7), (1, 7, −10), and (1, 8, −13) lie on the sameline?

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Q: Find a + b, 2a + 3b, lal, and la - b|. a = (4, –3), b = (-2, 5) a + b = (9,2) (2,9) 2a + 3b =

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Q: (5,19),(8,18),(10,14),(12,7) find the value of r and round to four decimals

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Q: Simplify. (4y²– 2y-3)+(3y²–5y-4)-(8)²-4y-8)

A: Given :

Q: .2 y = 4 - x² and x +y = 2.

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Q: Let á (5, 5) and 6 = (- 3, 1). - Find ā · 6

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Q: Let A = { 1, 2, 3, 4 } and B = { 4, 6, 8, 10 }. Find A x B

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Q: If x &gt; 4 and y &gt; 4, then x + y &gt; 8.

A: Since, we have been given that:-x&gt;4 -(i)y&gt;4 -(ii)Our Aim is to Prove that:- x+y&gt;8

Q: Let a = (-1,0, 5) and 6 = (3,-1,0). Find à x 6. < V

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Q: Let a = and b = . Find - à - b.

A: Given :a→=5, -5, -1b→=-4, 4, 0

Q: -7 3 Let A= -4 -3 Find 5A. 5A = %3D

A: We have to find 5A where it is given that: A=-73-4-3 In multiplication by scalar into the matrix we…

Q: 42- 12 20

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Q: a. If the sample correlation coefficient between X and Y is positive, then the slope of the…

A: a. If the sample correlation coefficient between X and Y is positive, then the slope of the…

Q: -1 2 5 2 7 -5 Let B = and C = 2 5 3 2 3 5 Find -4B+ 5C.

A: We have, B = -125253 C = 27-5235 To evaluate: The value of -4B+5C

Q: If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

A: We will write the products as coordinates where the first element will be from G and the second…

Q: Determine x and y such that -2 4 -2 + -6 -4 -1 1 2 4 4 2x +y x = y =

A: When two matrices are added, then their corresponding elements are added. For example, abcd+efgh=a+e…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.