In parts a-d evaluate the following determinants. show all steps. a. 2x2 matrix the first row...

In parts a-d evaluate the following determinants. show all steps.

a. 2x2 matrix the first row being 1 and 2 the second row being -3 and 4.

b. 3x3 matrix, the first row being 2,1, 5, the second row being 0, 3, 2, the third row being 0, 0, 4.

c. 3x3 matrix, the first row being 3, -1, 4, the second row being 2, -2, 3, the third row being 1, -1, 2

d. 4x4 matrix, the first row being 1, 1, 0, 3, the second row being 0, 2, 0, 0, the third row being 0, 3, -2, 1, the fourth row being 0, 4, 3, 2.

e. Which matrices in parts a-d are invertible? how do you know? show all steps.

Expert Solution

Colby Messinger answered 2 years ago

Perform all the steps for ALL PARTS (a - d) in R code and show and...

Perform all the steps for ALL PARTS (a - d) in R code and show and explain the results. Thank you. Problem 2.23 Consider the simple linear regression model y = 50 + 10x + E where E is NID(0,16). Suppose that the n = 20 pairs of observations are used to fit this model. Generate 500 samples of 20 observations, drawing one observation for each level of x = 0.5,1, 1.5, 2, ..., 10 [i.e. going up by an...

Please solve all parts of the following question. Please show all work and all steps. 1a.)...

Please solve all parts of the following question. Please show all work and all steps. 1a.) Solve x' = x + 3y + 2t y' = x - y + t^2 1b.) Solve x' + ty = -1 y' + x' = 2 1c.) Solve x' + y = 3t y' - tx' = 0

Please answer all parts of the question. Please show all work and all steps. 1a.) Show...

Please answer all parts of the question. Please show all work and all steps. 1a.) Show that the solutions of x' = arc tan (x) + t cannot have maxima 1b.) Find the value of a such that the existence and uniqueness theorem applies to the ivp x' = (3/2)((|x|)^(1/3)), x(0) = a. 1c.) Find the limits, as t approaches both positive infinity and negative infinity, of the solution Φ(t) of the ivp x' = (x+2)(1-x^4), x(0) = 0

Given the matrix A (2x2 matrix taking the first two column vectors from the input file),...

Given the matrix A (2x2 matrix taking the first two column vectors from the input file), compute the followings. Λ: the diagonal matrix whose diagonal elements are the corresponding eignevalues Λii = λi for i=1,2 R: the 2x2 matrix whose ith column vector is the eigenvector corresponding to λi for i=1,2 RΛRT: the matrix compositions 1/0: the comparison between A and RΛRT (is A= RΛRT?) Your output should have seven lines where the first two lines correspond to the 2x2...

Write a program which reads the matrix A (2x2 matrix taking the first two column vectors...

Write a program which reads the matrix A (2x2 matrix taking the first two column vectors from the input file) and the vector b (the third column vector) and solve for x in Ax=b for general A. If there is a unique solution, your output should be a 2x2 matrix with two lines and two numbers per line. The output should contain numbers with up to four significant digits. If the system is unsolvable or inconsistent, then your output should...

Find the basis for the row space, columnspace, and nullspace for the following matrix. Row 1...

Find the basis for the row space, columnspace, and nullspace for the following matrix. Row 1 {3,4,0,7} Row 2 {1,-5,2,-2} Row 3 {-1,4,0,3} Row 4 {1,-1,2,2}

show that a 2x2 complex matrix A is nilpotent if and only if Tr(A)=0 and Tr(A^2)=0....

show that a 2x2 complex matrix A is nilpotent if and only if Tr(A)=0 and Tr(A^2)=0. give an example of a complex 2x2 matrix which is not nilpotent but whose trace is 0

The following matrix is in reduced row echelon form. Decode from the matrix the solution of...

The following matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations or state that the system is inconsistent. (If the system is dependent assign the free variable the parameter t. If the system is inconsistent, enter INCONSISTENT.) 1 0 5 −4 0 1 −8 10 0 0 0 0 (x1, x2, x3) =

Let B equal the matrix below: [{1,0,0},{0,3,2},{2,-2,-1}] (1,0,0 is the first row of the matrix B)...

Let B equal the matrix below: [{1,0,0},{0,3,2},{2,-2,-1}] (1,0,0 is the first row of the matrix B) (0,3,2 is the 2nd row of the matrix B (2,-2,-1 is the third row of the matrix B.) 1) Determine the eigenvalues and associated eigenvectors of B. State both the algebraic and geometric multiplicity of the eigenvalues. 2) The matrix is defective. Nonetheless, find the general solution to the system x’ = Bx. (x is a vector)

II. Show all of your work in each question. In parts (d), (e), and (g) make...

II. Show all of your work in each question. In parts (d), (e), and (g) make sure to set up your null and alternative hypotheses and write your conclusions. Also, please round your numbers to 2 decimal points. Write legibly and neatly. III. You can use p-value approach or critical-value approach in writing the conclusions of your hypotheses. A large firm employing tens of thousands of workers has been accused of discriminating against its female managers. The accusation is based...

Question