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.
Answer:
He ate 42 of the 90 grapes in the bowl
The percentage of grape he ate will be given as this:
42/90 * 100%
=46.67%
Tyler has ate 46.67% of the grapes
Answer:
Model B has 6 shaded sections
Step-by-step explanation:
The question is not complete. The complete question should be in the form:
Victor has 2 fraction models. Each is divided into equal sized sections the models are shaded to represent the same fraction. Model A is divided into 6 sections and 3 sections are shaded. Model B is divided into 12 sections. What do you know about the number of sections shaded in Model B? Explain your answer.
Solution:
The fraction modeled by model A is given by the ratio of shaded sections to the total number of sections.
That is Fraction of model A = number of shaded sections / total number of sections.
Hence:
Fraction of model A = 3 / 6
Since model B and Model A are equivalent, the number of shaded sections in Model A is given by:
number of shaded sections in model B/ total number of sections in model B = Fraction of model A
number of shaded sections in model B / 12 = 3 / 6
number of shaded sections in model B = 12 * 3/6
number of shaded sections in model B = 6
First you would put both numbers into improper fractions.
3 1/3 = 10/3 and 2 1/4 = 9/4
Multiply 10/3 * 9/4
10*9 = 90 and 3 * 4 =12
So 90/12 is your fraction. Reduce it, 7 6/12
7 6/12 = 7 1/2
So your answer is 7 1/2
Hope I helped :)
