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4 years ago

6

String A is 1 yard shorter than string B. String C is 1 ft 8 inches shorter than string B.

1 answer:

pentagon [3]4 years ago

3 0

Let the length of string A be x
it is 1 yard = 3 ft shorter than string B
so length of string B = x+3

String C is 1ft 8 inches shorter than B,
so C = x+ 1ft 8 inch = x+ 1+ 2/3 ft.

Total of A +B+C = 13ft 4inch = 13 + 1/3 ft.

x + x+3 + x+1+2/3 = 13 + 1/3
3x + 4 + 2/3 -1/3 = 13
3x = 13 - 4- 1/3
3x = 9 -1/3
x = 3 -1/9
x = 3ft - 12/9 inches = 3 ft - 4/3 inches
x = 2.889 ft

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3 years ago

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3 years ago

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4 years ago

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yan [13]

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3 years ago

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Lerok [7]

We found a counterexample, so the statement is false.

<h3>Is the statement true?</h3>

Let's use the matrix:

$\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right]$

This is a 4x4 matrix with determinant equal to -2.

The inverse matrix is:

$\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right]$

If we multiply it by 2, we get:

$\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right]$

The adjoint of that is the original matrix, actually:

$\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right]$

Which we already know, has a determinant of -2.

So the statement is false, as we found a counterexample.

If you want to learn more about matrices:

brainly.com/question/11989522

#SPJ1

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2 years ago