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Artyom0805 [142]
3 years ago
5

When calculating the determinant of a matrix, the answer is a single number rather than a matrix.

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
5 0

Answer:

Yes, one of the properties of determinants is that they are real numbers (including zero) not matrix. This if the entries of the matrix are real. Determinants can be both positive or negative numbers.

Step-by-step explanation:

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The unknown b is stuck in the exponent position.
We can can fix that by using logarithms.
Log is the inverse operation of the exponential.

We'll take log of each side.
Log of what base tho?

Well, the base of our exponential is e,
so we'll take log base e of each side.

\rm log_e(5)=log_e(e^{3b})

We'll apply one of our log rules next:
\rm \log(x^y)=y\cdot\log(x)

This allows us to take the exponent out of the log,

\rm log_e(5)=(3b)log_e(e)

Another thing to remember about logs:
When the base of the log matches the inside of the log,
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So our equation simplifies to this,

\rm log_e(5)=(3b)\cdot1

As a final step, divide both sides by 3,

\rm \frac13log_e(5)=b

k, hope that helps!


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