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musickatia [10]
3 years ago
8

Can you think of any 2x2 matrices d for which cd = dc for all 2x2 matrices c? give 2 different examples of such matricesd.

Mathematics
1 answer:
Ksju [112]3 years ago
6 0
For any arbitrary 2x2 matrices \mathbf C and \mathbf D, only one choice of \mathbf D exists to satisfy \mathbf{CD}=\mathbf{DC}, which is the identity matrix.

There is no other matrix that would work unless we place some more restrictions on \mathbf C. One such restriction would be to ensure that \mathbf C is not singular, or its determinant is non-zero. Then this matrix has an inverse, and taking \mathbf D=\mathbf C^{-1} we'd get equality.
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DUPLICATE. WITH ATTACHMENTS
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3 years ago
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Consider the logarithms base 5. For each logarithmic expression below, either calculate the value of the expression or explain w
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Answer:

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Step-by-step explanation:

Given:

log₅(3125)

Now,

using the property of log function that

logₐ(b) = \frac{\log(b)}{\log(a)}

thus,

Therefore, applying the above property, we get

⇒ \frac{\log(3125)}{\log(5)}   (here log = log base 10)

now,

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thus,

⇒  \frac{\log(5^5)}{\log(5)}

Now,

we know from the properties of log function that

log(aᵇ) = b × log(a)

therefore applying the above property we get

⇒ \frac{5\log(5)}{\log(5)}

or

⇒ 5

Hence,

log₅(3125) = 5

8 0
3 years ago
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