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# 数学代写｜MATH1113 Quiz Tutorial 01 – Mathematical foundations

## Quiz Instructions

Numeric answers that are not integers should be reported to 2 decimal places.

### Question 1             1pts

What is the trace of matrix m (defined in the R script)?

### Question 2            1pts

What is the trace of a 10 by 10 identity matrix?

### Question 3           1pts

What is the product of the elements in column vector V (defined in the R script)?

### Question 4           1pts

What is the value of the element in matrix m in row 4 and column 6?

### Question 5           1pts

What is the average of the second column of matrix m?

### Question 6           1pts

What is the maximum value in the third row of matrix m?

### Question 7           1pts

What is the number of columns in matrix m plus the number of rows in matrix m?

### Question 8           1pts

A) Create variable called row5 equal to row 5 of matrix m.
B) What is the the result of multiplying row5 by v?

### Question 9           1pts

What is the scalar value resulting from multiplying the transpose of column “X_ .1″
in data frame f by column”X_ _2” in f?
The data frame f is defined in the provided R script.

### Question 10           1pts

Randomly generate 10000 values for variable y using the model:
y= 1+2x+ e
where:
●X isa normally distributed random variable with mean 0 and variance 1
●e is a normally distributed random variable with mean 0 and variance 1
●X and e are independent random variables

What is the absolute value of the difference between your sample variance of y and the population variance of y, given the model for y and the distributions of X and e?