Question: Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A.

Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A.

Step by Step Solution

★★★★★

3.43 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Suppose that the characteristic po... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

961-M-L-A-L-S (6064).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Suppose that A is a square matrix, and B is a matrix in reduced row-echelon form that is row-equivalent to A. Prove that if A is singular, then the last row of B is a zero row.

Q:

Suppose that A is a square matrix of size n n and that we know there is a single vector b Cn such that the system LS(A, b) has a unique solution. Prove that A is a nonsingular matrix.

Q:

Suppose that A is a square matrix and there is a vector, b, such that LS(A, b) has a unique solution. Prove that A is nonsingular. Give a direct proof (perhaps appealing to Theorem PSPHS) rather than...

Q:

I Find the (real) eigenvalues and associated eigenvectors of each matrix. Find a basis for each eigenspace of dimension 2 or larger. 7 (a) 12 -10 3 5 -2 (b) C 0 II Suppose A is a 2 X 2 matrix. Show...

Q:

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

Q:

(a) Suppose that A is a 3 x 3 diagonalizable matrix with a basis of eigenvectors of R given by {u?, U?, U3} with corresponding eigenvalues A1, A2, A3. Suppose that the matrix B is also a 3 x 3...

Q:

(a) Show that a matrix is invertible if and only if the constant term in its minimal polynomial is not 0. (b) Show that if a square matrix T is not invertible then there is a nonzero matrix S such...

Q:

Suppose that A is square matrix, prove that: the sum of its eigenvalues is equal to the trace of A; the product of its eigenvalues is equal to the determinant of A.

Q:

(5) (6 Points total) Suppose that a square matrix C has a characteristic polynomial equal to (x - 1)(x - 2)3(x -3)3. (a) (1 Point) What are the dimensions of C? Answer: (b) (1 Point) What are the...

Q:

Show steps (5) (6 Points total) Suppose that a square matrix C has a characteristic polynomial equal to (x - 1) (2 + 2) 3 (x - 3) 5. (a) (1 Point) What are the dimensions of C? Answer: (b) (1 Point )...

Q:

A firm has the following short run demand and cost schedule for a product. Q = 200 5P TC = 400 + 4Q a. What are price, quantity and profit for this company? b. Suppose the above demand shifted to Q...

Q:

Firm Valuation (v3) The Obermann family privately owns what has historically been a very successful incorporated enterprise. Due to the recent pandemic crisis however the last year has proven to be...

Q:

An organization has forecasted maximum production requirements for the coming year as follows: January 400 July 580 February 510 August 600 March 400 September 300 April 405 October 280 May 460...

Q:

7. Suppose the following table describes Jocelyns weekly snack purchases, which vary depending on the price of a bag of chips: a. Compute the cross price elasticity of salsa with respect to the price...

Q:

(a) Write out a pseudo-code algorithm, using both row and column pointers, for Gaussian Elimination with Full Pivoting. (b) Implement your code on a computer, and try it on the systems in Exercise...

Q:

Implement the computer experiment with Hilbert matrices outlined in the last paragraph of the section.

Q:

Let Hn be the n à n Hilbert matrix (1.70), and Kn = H-ln its inverse. It can be proved, [32, p. 513], that the (i, j) entry of Kn is Where is the standard binomial coefficient. (a) Write down...

Q:

Is there a program online i can use to make a 3D version of a 2 and 3 hole torus. Something like this but in 3D 00

Q:

Which of the following is a good example of a cognitive algorithm?

Q:

The marketing team at an internet music site wants a better understanding of who their customers are. They send out a survey to 25 customers(and use an incentive of$50 worth of downloads to guarantee...