Question: Let A be a nonsingular n n matrix and let be an eigenvalue of A. (a) Show that 0. (b) Show

Let A be a nonsingular n × n matrix and let λ be an eigenvalue of A.
(a) Show that λ ≠ 0.
(b) Show that 1/λ is an eigenvalue of A-1.

Step by Step Solution

★★★★★

3.41 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a det A 1 2 n If A is nonsingular then det A 0 and hence all of ... 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

949-M-L-A-E (896).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let A be a nonsingular n n matrix. Use mathematical induction to prove that Am is nonsingular and (Am)-1 = (A-1)m for m = 1, 2, 3, ...

Q:

Let A be a nonsingular n n matrix and let B be an n r matrix. Show that the reduced row echelon form of (A|B) is (I|C), where C = A-1B.

Q:

Let A be a nonsingular n n matrix with n > 1. Show that det(adj A) = (det(A))n-1

Q:

Let A be a nonsingular n n matrix and let Q be an n n orthogonal matrix. Show that (a) cond2(QA) = cond2(Ag) = cond2(A) (b) If B = QTAQ, then cond2(S) = cond2(A).

Q:

Let A be a symmetric positive definite n n matrix and let S be a nonsingular n n matrix. Show that STAS is positive definite.

Q:

Let x1,..., xk be linearly independent vectors in Rn, and let A be a nonsingular n n matrix. Define yi = Axi for i = 1,....,k. Show that y1,....,yk are linearly independent.

Q:

Let D be a nonsingular n à n diagonal matrix and let (a) Show that (b) Show that and dmin-min ldil dmax=max ld,il Isisn condi( D) = condoo (D) =-max dmax dmin cond2(D) =

Q:

1. (4 Points) Let x and y be vectors in R". None of the given choices. O If [x) + lyl = [x + yl. then x and y are parallel. If x . y = 1, then x and y are parallel. O If [x x yl = 1, then x and y are...

Q:

Q9some type is wrong, can refer to the attach file. In a study of the relationship between an explanatory variable Z and a response variable Y , n independent observations are taken in the form of...

Q:

7.11 7.11 Assume A is a nonsingular n n matrix. Show that thee inverse of the matrix A AA-T MI = is given by -AT A-1+AT AT (12) (a) Compare the complexity of the following two methods for solving a...

Q:

Figure shows a cross section of a long conducting coaxial cable and gives its radii (a, b, c). Equal but opposite currents i are uniformly distributed in the two conductors. Derive expressions for...

Q:

Toy Country Corporation produces childrens toys using a liquid plastic formula and a continuous production process. In the companys toy truck work cell, the plastic is heated and fed into a molding...

Q:

Redesign the same RAM - based 7 - segment decoder as in Apply 8 A , this time using four separate 4 x 8 RAM blocks. The RAM blocks each contain characters 0 to 3 , 4 to 7 , 8 to 1 1 , and 1 2 to 1 5...

Q:

Describe the circular flow model of the economy, including the expenditure side and the income side, as well as all of the leakages and injections in the model.

Q:

Let L1 and L2 be linear transformations from a vector space V into a vector space W. Let {v1, v2 ... vn} be a basis for V. Show that if L1 (v,) = L2 (v) for i = 1, 2 . . . n, then L1 (v) = L2 (v) for...

Q:

Let L: V W be a linear transformation from a vector space V into a vector space W. The pre-image of a subspace W1 of W is defined as

Q:

Let O: Rn Rn be the zero linear transformation defined by O (v) = 0 for v in Rn. Find the standard matrix representing O.

Q:

What is the Macaulay duration of a 7% coupon bond with 5 years to maturity and a yield to maturity of 6.4%?

Q:

Question 3. (15 points) Suppose you apply a 5-year bank loan of $400,000 at 12% APR, repayable in equal instalments at the end of each month. Assume that you pay $8,897.779 each month. a. How much is...

Q:

Find the triangular arbitrage and the Covered Interest Arbitrage of the following : knowing that the spot rate of the euro is 0.8835 and the interest rate of the Euro Area is 0% and the one of the...