Let W. Z V be complementary subspaces in a vector space V, as in Exercise 2.2.24.
Question:
(a) Prove that if (w1,...,wj} form a basis for W and {z1.......zk} a basis for Z, then {w1,..., wj, z1,.... zk} form a basis for V.
(b) Prove that dim W + dim Z = dim V.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 61% (13 reviews)
a Every v V can be uniquely decomposed as v w z where w W z Z Write w c 1 w 1 c j w j and z d 1 z 1 ...View the full answer
Answered By
Munir Ahmed Jakhro
I am professional Tutor of of Business Courses, I did my four years Bachelor Degree from one of the Top Business schools of World "Institute of Business Administration" in year 2013. Since then I have been working as Tutor of Accounting, Finance tutor on different online platforms like this website. I am have experience of 6 years teaching business courses to students online and offline my professional job at national savings also helped me in accounting understanding .
4.90+
8+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Let W V be a subspace. A subspace Z V is called a complementary subspace to W if (i) W Z = {0}, and (ii) W + Z = V, i .e., every v V can be written as v = w + z for w W and z Z. (a) Show that...
-
(a) Show that V0 = ( (v, 0) | v V ) and w0 = ( (0, w) | w e w ) are complementary subspaces, as in Exercise 2.2.24, of the Cartesian product space V W, as defined in Exercise 2.1.13. (b) Prove that...
-
A projection matrix is a square matrix P that satisfies P2 = P. (a) Prove that w mg P if and only if P w = w. (b) Show that mg P and ker P are complementary subspaces, as defined in Exercise 2.2.24,...
-
Air flows through the fine mesh gauze shown in the figure below with an average velocity of 1.50 m/s in the pipe. Determine the loss coefficient for the gauze. KL= i 8.1mm V = 1.5 m/s Water Gauze...
-
Briefly discuss the difference between authority and responsibility
-
Make a harmonic analysis of the function shown in Fig. 1.119 including the first three harmonics. Force (N) 40 30 20 10 0 -10 -20 -30 -40 0 0.1 0.2 0.3 Time (s) 0.4 0.5 0.6 FIGURE 1.119 Graph showing...
-
The principle of increase in entropy is concerned with (a) Reversible processes (b) Irreversible processes (c) Quasi-static process (d) None of these.
-
Connie Young, an architect, opened an office on October 1, 2019. During the month, she completed the following transactions connected with her professional practice: a. Transferred cash from a...
-
4) Transactions for the month of July for Shelly's Bookstore were as follows: Purchases Salca July 1 (balance) 600 8 $7.30 1,200 @ $7.40 July 3 350 @$9.50 12 900 @9.75 22 700 $7.60 25 800 10.00 250...
-
What is the relationship between funding cost and funding or withdrawal risk?
-
Let W V be a subspace. (a) Prove that dim W < dim V. (b) Prove that if dim W = dim V = n < , then W = V. Equivalently, if W V is a proper subspace of a finite-dimensional vector space, then dim W <...
-
Let f1(x),..., fn(x) be scalar functions. Suppose that every set of sample points x1, . . . ,xm R, for all finite m 1, leads to linearly dependent sample vectors f1.......fn Rm. Prove that...
-
Which of the following is a preventive control? a. Training b. Log analysis c. CIRT d. Virtualization
-
How do courts assess the fairness and feasibility of reorganization plans?
-
List the priority of claims for the distribution of a liquidated firms assets.
-
Indicate whether each of the following statements is true or false by writing T or F in the answer c olumn. One of the primary purposes of setting up a trust is to receive favorable tax treatment.
-
What are some differences between the NYSE and the NASDAQ stock market?
-
What are junk bonds?
-
Lunar Corporation issued $80,000 in bonds for $87,000 on Jan. 1. The bonds had a stated rate of 8% and pay interest quarterly. What is the journal entry to record the first interest payment?
-
After looking at the resources, explain what a spirit image is. Why might looking at a god and/or a human in terms of their spirit be helpful if you want to eliminate some of the divisions between...
-
Show that evaluating the determinant of an n à n matrix by cofactors involves (n! - l) additions and multiplications. 11/ k=1
-
Show that the elimination method of computing the value of the determinant of an n n matrix involves [n(n - 1)(2n - l)]/6 additions and [(n - 1)(n2 + n + 3)]/3 multiplications and divisions.
-
Let A be an n n matrix and a scalar. Show that det(A) = n det(A)
-
Use the table for the question(s) below. Suppose the term structure of interest rates is shown below: Term Rate 1 year 2 years 3 years 5 years 10 years 20 years (EAR%) 5.00% 4.80% 4.60% 4.50% 4.25%...
-
Alpha and Beta Companies can borrow for a five-year term at the following rates: Alpha Beta Moody's credit rating Aa Baa Fixed-rate borrowing cost 10.5% 12.0% Floating-rate borrowing cost LIBOR...
-
4) Transactions for the month of July for Shelly's Bookstore were as follows: Purchases Salca July 1 (balance) 600 8 $7.30 1,200 @ $7.40 July 3 350 @$9.50 12 900 @9.75 22 700 $7.60 25 800 10.00 250...
Study smarter with the SolutionInn App