Suppose A is a nonsingular n x n matrix. (a) Prove that any n x (n +
Question:
(a) Prove that any n x (n + k) matrix of the form (A B), where B has size n à k. has rank n.
(b) Prove that any (n + k) Ã n matrix of the form
where C has size k à n, has rank n.
Transcribed Image Text:
A
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 81% (11 reviews)
a Since they are spanned by the columns the rang...View the full answer
Answered By
Aqib Parvej
I am teaching since my graduation time so I have teaching experience of about 5 years and in these years I learn to teach in the best and interesting way .
4.80+
20+ Reviews
41+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
The trace of a n à n matrix A MnÃn. is defined to be the sum of its diagonal entries: tr A = a11 + a22 + + ann. (a) Compute the trace of (b) Prove that tr(A + B) = tr A + tr B. (c)...
-
Suppose A is an m x n matrix, and B and C are nonsingular matrices of sizes m m and n n, respectively. Prove that rank A = rank B A = rank A C = rank B AC.
-
(a) Prove that for any 2 Ã 2 matrix T there are scalars c0, . . . , c4 that are not all 0 such that the combination c4T4 + c3T3 + c2T2 + c1T + c0I is the zero matrix (where I is the 2 Ã...
-
Use the correlation matrix from Problem 1 to answer the following questions. a. Compute the semipartial rSBP(SMK|AGE). b. Compute the semipartial rSMK(SBP|AGE). c. Compare these correlations to the...
-
Thomsett suggests that there are 2 distinctly different types of risks. Explain what he means by project and business risks. Which class of risk causes the most problems? Why?
-
Pick a country (other than Mexico) and show how significant historical events have affected the countrys culture.
-
Consider a source of flow in \(3 \mathrm{D}\) of strength \(S\) (dimensions \(L^{3} / T\) ), Then the flow is axisymmetric and independent of the \(\theta\)-direction in the spherical coordinate...
-
Susan Varhard, treasurer of the Gammamax Company, has proposed that the company should sell equity and buy back debt in order to maximize its value. As evidence, she presents the financial statements...
-
1. How would you describe the basic components of WACC to a group of decision makers in a company? 2. On the most basic level, if a firm's WACC is 12 percent, what does this mean? 3. In calculating...
-
Your client has asked your advice regarding a recent property sale. Are you required to communicate the advice in writing?
-
Suppose is a particular solution to the equation (a) What is b? (b) Find the general solution 123 0 01-1
-
Let A be an m x n matrix of rank r. Suppose v1,. . . vn are a basis for Rn such that vr+1.......vn form a basis for ker A. Prove that w1 = Av1.... . wr = Avr, form a basis for mg A.
-
Danier needs to be skillful in negotiating purchase contracts with suppliers. What shipping terms should Danier negotiate to minimize its freight-in costs?
-
Agatha's Murder Inc. has just purchased and installed a piece of equipment for $1,000,000. The equipment can be sold off at the end of 5 years for $120,000. For tax purposes, the equipment belongs to...
-
TenTen Ltd. has a 7-year, 6% semi-annual coupon bonds. These bonds are currently trading at a price of $1,050. What is the company's after-tax component cost of debt? Assume no flotation costs and a...
-
The 6-month $730 strike call premium is $60 and the 6-month $830 strike call on the same underlying asset is selling for $30. A strategy consists of longing the 730-strike call and shorting the...
-
The forecast for the free cash flows for Jimi's Vinyl Records for 2023 are provided below. Assume that free cash flow is paid at the end of each year and we are at the beginning of year 2023. Because...
-
Currency pair: EUR/USD (1.09793/1.09806) Long or Short: Long 1 lot of EUR/USD in CFDs Open price (ask): 1.09806 Trade size: 100,000 Leverage: 10:1 Margin: 10% Balance in account: $15,000 a) Calculate...
-
An absolute pressure gauge is submerged 50 m (1979 inches) below the surface of the ocean and reads P = 6.064 bar. This is P = 2434(inches of H 2 O), according to the unit conversions built into a...
-
Review Exhibit 11.4. Analyze each product on the graph according to the characteristics that influence the rate of adoption. For example, what can you conclude from the data about the relative...
-
Let [u1, u2] and [v1, v2] be ordered bases for R2. Where (a) Determine the transition matrix corresponding to change of basis from the standard basis [e1,e2] to the ordered basis [111,112]. Use this...
-
For each of the following determine whether the given set is a subspace of R2. Prove your answers. (a) (b) x2 | .ri +.x2 = () S2=
-
Given (a) Find a basis for N(A) (the null space of A). What is the dimension of N(A)? (b) Find a basis for the column space of A. What is the rank of A? 4123 3123 1123 3000 1000
-
PART A (Retained Earnings Statement) January 1, Retained Earnings Beginning Balance 2021 Income before income tax 1 $2,340,000 Prior period adjustment: understatement of 2020 depreciation expense...
-
There are 3 source and 4 destinations, For the data below, construct an initial feasible solution. Cost Destination 1 Destination 2 Destination 3 Destination 4 Supply Source 1 12 18 9 11 105 Source 2...
-
A company is using Dynamics 3 6 5 Project Operations. You acquire an independent software vendor ( ISV ) solution from AppSource that contains several project charts and install the solution in the...
Study smarter with the SolutionInn App