Question: In each case either prove the statement or give an example showing that it is false: (a) If A is invertible and adj A =

In each case either prove the statement or give an example showing that it is false:
(a) If A is invertible and adj A = A-1, then det A = 1.
(b) If det A ≠ 0 and AB = AC, then B = C.
(c) If adj A = 0, then A = 0.
(d) If A has a row of zeros, so also does adj A.
(e) det(I + A) = 1 + det A.
(f) If det A = 1, then adj A = A.

Step by Step Solution

★★★★★

3.50 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a True Write d detA so that d A 1 adj A Since adj A ... View full answer

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)

950-M-L-A-L-S (6320).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

In each case either prove the statement or give an example in which it is false. Throughout, let T: V W be a linear transformation where V and W are finite dimensional. (a) If V = W, then ker T im...

In each case either prove the result by splitting into cases, or give a counterexample. (a) If n is any integer, then n2 = 4k + 1 for some integer k. (b) If n is any odd integer, then n2 = 4k + 1 for...

In each case either show that the statement is true or give an example showing that it is false. (a) If U Rn is a subspace of Rn and X+ Y is in U, then X and F are both in U. (b) If U is a subspace...

In each case either prove the statement or give an example showing that it is false: (a) If det A = 0, then A has two equal rows. (b) If R is the reduced row-echelon form of A, then det A = det R....

As I am very familiar with the system, please read the instructions and kindly follow each single one of them: If you are not an (Engineering proficient with Masters's or above, please, do not take...

Consider a system of linear equations with augmented matrix A and coefficient matrix C. In each case either prove the statement or give an example showing that it is false. (a) If there is more than...

In each case either prove the statement or give an example showing that it is false. (a) If || - || = 0, then = . (b) If |||| = ||||, then = . (c) If = t for some scalar t, then and have the same...

In each case either prove the assertion or give an example showing that it is false. (a) If A and B are both invertible, then A + B is invertible. (b) If A4 = 3I, then A is invertible. (c) If AB = B...

In each case, either prove the assertion or give an example showing that it is false. (a) P2 has a basis of polynomials f(x) such that f(b) = 0. (b) Every basis of M22 contains a noninvertible...

In three phase induction motor when rotor speed is not equal to stator rotating magnetic field speed then flux linkages are zero and hence emf induced in rotor conductors are zero. Select one: O True...

In referring to Startup Weekend, someone made the comment Its not a start-up factory, its an entrepreneur factory. What do you think the person meant by that comment?

What are the two ways in which a firm can grow?

In what ways do extensions of the project managers role into activities, such as business case development and postimplementation benefit delivery, require capability development? What management...

Let S be an m n matrix and let b Rm. Show that b R(A) if and only if b =AA+b

If a, b, and c are floating - point numbers, then fl(fl(a + b) + c) = fl(a + fl(b + c)) In the case of a true statement, explain or prove your answer. In the case of a false statement, give an...

If two m n matrices A and B are close in the sense that ||A - B||2

The YTM on a bond is the interest rate you earn on your investment if interest rates dont change. If you actually sell the bond before it matures, your realized return is known as the holding period...

5 marks 3. Consider the set T whose elements are all the factors of 1000 and denote a relation 1' C T x T such that orb if a is a factor of b. i. Verify that (T,1') is a poset. ii. Give the least...

Dantzler Corporation is a fast-growing supplier of office products. Analysts project the following free cash flows (FCFs) during the next 3 years, after which FCF is expected to grow at a constant 4%...