Answer:
exactly one, 0's, triangular matrix, product and 1.
Step-by-step explanation:
So, let us first fill in the gap in the question below. Note that the capitalized words are the words to be filled in the gap and the ones in brackets too.
"An elementary ntimesn scaling matrix with k on the diagonal is the same as the ntimesn identity matrix with EXACTLY ONE of the (0's) replaced with some number k. This means it is TRIANGULAR MATRIX, and so its determinant is the PRODUCT of its diagonal entries. Thus, the determinant of an elementary scaling matrix with k on the diagonal is (1).
Here, one of the zeros in the identity matrix will surely be replaced by one. That is to say, the determinants = 1 × 1 × 1 => 1. Thus, it is a a triangular matrix.
With the whole question ???
A fraternity name formed by two letters would have 24 choices for the first letter, and 24 choices for the second, therefore 24*24=576 is the correct answer.
Answers:
Answer for row one: 1
Answer for row two: 11
Answer for row three: 16
Answer for row four: 36
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Work Shown:
Whatever the x value is, we multiply by 5 and subtract off 14 to get the corresponding y value. This is following the order of operations PEMDAS
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If x = 3, then
y = 5*x - 14
y = 5*3 - 14 ..... note how x is replaced with 3
y = 15 - 14
y = 1
This means that when x = 3, the y value is y = 1.
So 1 goes in the box in the first row.
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Repeat for x = 5
y = 5*x - 14
y = 5*5 - 14
y = 25 - 14
y = 11
We have 11 as the second answer.
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Repeat for x = 6
y = 5*x - 14
y = 5*6 - 14
y = 30 - 14
y = 16
The third answer is 16.
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Repeat for x = 10
y = 5*x - 14
y = 5*10 - 14
y = 50 - 14
y = 36
The last answer is 36.
