Six sophomores and 14 freshmen compete
1 answer:
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Answer: New function is
Step-by-step explanation:
- A dilation is a transformation that creates an image using a scale factor that has the exactly same shape as the original, but have a different size.
The given function :
We know that any function y= f(x) will become y=k f(x) after dilation of k units on the x, where k= scale factor for dilation.
Here, the given scale factor = 2 i.e. k=2
Then, the new function will be :
Hence, the new function is
Answer:
Yes, it is invertible
Step-by-step explanation:
We need to find in the matrix determinant is different from zero, since iif it is, that the matrix is invertible.
Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!
Then the determinant of this matrix becomes:
And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:
Therefore, the Det of the initial matrix is : 4 * 3 = 12
and then the matrix is invertible