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

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

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step-by-step explanation: