Jesus R.

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Linear Algebra

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Question:

The inverse of the matrix [ 4 3 ] is: [ 9 7 ]

Jesus R.

Answer:

The matrix A = [ a b ] is invertible if and only if ad - bc is not equal to 0, in which case the [ c d ] inverse is given by the formula A^ -1 = 1/ ad - bc [ d -b ]. Therefore. we have 7 * 4 - 9 * 3 = 28 -27 = 1. [ -c a ] We then have 1/1 [ 7 -3 ] which equals [ 7 -3 ] [ -9 4 ] [ -9 4 ]

Discrete Math

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Question:

Find the contrapositive of the following statement: If the product of two integers is even, then one of the two integers is even.

Jesus R.

Answer:

The original statement is in the form P->Q. To form the contrapositive, you must switch P and Q and negate them both. It will look like this: ~Q -> ~P. The answer would then be: If two integers are not even, then the product of the two integers is not even.

Statistics

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Question:

Find the sample mean of the given data: 6, 3, 7, 5, 1, 2, 5, 6, 9

Jesus R.

Answer:

You can find the sample mean by adding all the numbers and dividing by how many numbers you have. So we have 6 + 3 + 7 + 5 + 1 + 2 + 5 + 6 + 9 which gives us 44 and we divide that by 9 because that's how many numbers we are working with. This gives us 4.89., which is the final answer.

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