Show that if A , B, and C are square matrices, then det = (det A) (det

Question:

Show that if A , B, and C are square matrices, then det

= (det A) (det B).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:01 AM

See More Questions

Let where B and C are square matrices. (a) If Î» is an eigenvalue of B with eigenvector x = (x1,..., xk)T, show that Î» is also an eigenvalue of A with eigenvector = (x1,...,...
Show that if A and B are square matrices, then det = (det A)(det B). 8
Show that if A and B are similar, then det A = det B.
Consider the following table, which gives the running time T(n) in seconds for a program for various values of the input size n: a. What is the value of T(n) if n = 160007 10240 5120 40960 20480 B C...
Gina Fox is a student who will be graduating soon, and she is planning to attend graduate school to work toward an MBA. Gina has been accepted into the graduate programs at three universities. Now...
Office Automation, Inc., must choose between two copiers, the XX40 or the RH45. The XX40 costs $2,400 and will last for three years. The copier will require a real aftertax cost of $160 per year...
How would a company know that its product or service was preferred in the marketplace? What could a competitor do to erode this favorable position?
A He-Xe mixture containing 0.75 mole fraction of helium is used for cooling of electronics in an avionics application. At a temperature of 300 K and atmospheric pressure, calculate the mass fraction...
Provide 2 different ways of representing this problem and its solution that might be used to 'convince' a student of the solution and its reasonableness. Think about the different ways that fractions...
What are the main arguments Sarah is trying to counter? That is, what are the reasons and rationalizations she needs to address in deciding how to handle the meeting with Paul?
If A is a nonsingular matrix such that A2 = A, what is det(A)?
Use the properties of Section 3.2 to prove that laa
Knights Furniture sells furniture and electronic items. The majority of its business is on credit, and the following information is available relating to sales transactions for 2007, 2008, and 2009....
The demand (in thousands) for a product as a function of price p (in dollars) is given by d (p) = p - 2p+ 35 for 0 5. It is estimated that the cost of making this product is $2. a) What is the size...
2. Crohn's disease is a chronic inflammatory disease. A double-blind completely randomized experiment of 71 persons who were resistant to or intolerant to the standard therapy was conducted where 37...
Based on the financials, what was their cash balance for the most recent year, and how did it compare to the prior year? How much did they spend on R&D costs during the most recent year, and what was...
9. (a) Do there exists terms a, b, c, d R such that x + 1, x < 1 s(x) = { ax + bx+cx+d, x [1, 1] - x 1, is a natural cubic spline function? (b) Do there exists terms a, b, c, d R such that x > 1...
(15 points) Consider the system: -2 5 9 X1 (100-(0) 7 -37 X3 = -26 (1). Perform three iterations of the Jacobi method with your initial guess being the zero vector. Why does it not appear to be...
College Life produces sweatshirts for college organizations and uses hybrid costing. It reports the following for its fabrication process. Customers choose screen-printed or embroidered logos. a....
What are bounds and what do companies do with them?
Show that if T: V V is a contraction or a dilation of V(Example 4 of Section 8.1), then the matrix of T with respect to any basis for V is a positive scalar multiple of the identity matrix.
Prove that if B and B are the standard bases for Rn and Rm, respectively, then the matrix for a linear transformation T: Rn Rm with respect to the bases B and B is the standard matrix for T.
In each part, B = {f1, f2, f3} is a basis for a subspace V of the vector space of real-valued functions defined on the real line. Find the matrix with respect to B of the differentiation operator D:...
2. Consider a helicopter rotor in a wind tunnel. The rotor is spinning and the wind is turned on. The equation for the rotor flapping was derived in class for this situation. Note that = - +C/2 =...
In this problem, you are asked to go through the steps of a finite element analysis. The key features include the use of isoparametric element formulation and Gauss numerical integration. (A) Problem...
A wheel rolls without slipping on a surface with a constant radius of curvature R. The centre of curvature is located at point O. R 20 9 G m Assume the wheel can be approximated as a uniform disk...

Show that if A , B, and C are square matrices, then det = (det A) (det

Question:

A O C B

Step by Step Answer:

From Definition 32 the only time we get terms which do not contain a zero ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions