If A=[xy5−8] determine the values of x and y for which A2=A.

Matrices are used to represent data in rows and columns

The values of x and y are 9 and -14.4 respectively.

Matrix A is represented as:

Calculate

Recall that

This means that:

So, by comparison

Similarly

Hence, the values of x and y are 9 and -14.4 respectively.

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Step-by-step explanation:

Given the 2 by 2 matrix , we are to find the value of x and y for the expression A² = A to be true.

First we need to find A² by multiplying the same matrix together

Equating the first row and second column of both matrices together, we will have;

5x-40 = 5

add 40 to both sides of the equation

5x-40+40 = 5+40

5x = 45

x = 45/5

x = 9

Similarly,  we will equate the second row and second column of both matrices to have;

5y+64 = -8

Subtract 64 from both sdies

5y+64-64 = -8-64

5y = -72

y = -72/5

Hence the value of x is 9 and y is -72/5

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step-by-step explanation:

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b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.