線型空間論の問題です。 詳しく解説していただけるととてもありがたいです。 よろしくお願いします🙏🙏

[3] (異なる固有値に対する固有ベクトルは直交する) A∈ Man (R)が対称行列 ('A=A) とする。 x,y∈R” に対 し、対称2次形式を、 で定める。 <x,y>='xÂy また、α,βERが、 A の固有値であって、 α≠βであると し、 x ∈R” がα についての固有ベクトル, yeR” が β に ついての固有ベクトルであるとする。 (1) このとき、 'xA = 'x Ay=By であることを確かめなさい。 (2) さらに、 < x, y >= axAy=β'xAy を確かめ、 <x,y >= 0, 'xy = 0 であることを示しなさい。

かっこの中が分からないです。

Exercise Task 1: Look at the following. What word goes into the space? The same word goes into the spaces for both sentences, a and b. 次の各文を読んでください。 空欄に入る単語は何ですか。 aとb、両方の文の空欄には同じ単 が入ります。 a. Jim presented her boss with a list of. s from the staff. 1) b. There is a lot of _______ for larger mobile phones. 2) a. Where do you do your grocery. b. Please put the __________ in the trunk. ? 2) 3) a. A short at the end of a paragraph can be better than 3). a long one. b. The judge gave the murderer a life 4) a. - generally starts in March in the Northern 4). Hemisphere. b. There's a natural on this mountain. 5) a. You don't need to the bell. Just come in. 5) b. Can you me on the telephone tonight? b. My 6) a. These books are Jane's ____. 7) a. We have a ________ to help each other. 8) a. Yuki often wears a straw 6) b. The realtor came to assess the value of the 7) is cleaning the toilets. in the summer. 8) b. I have to wear two _s, my teacher __________ and my researcher.

（2)についての向きがよく分かりません。 解説を見てもどうゆう考えでこう書いているのか分からないので、教えて欲しいです。 全く想像できてない状態です。

-2=160=4 北は攻へ右ねじを回すとき、 ねじが進む向き

英語の問題です。 教えて欲しいです🙇‍♀️

(2) I had my teeth 1 check 1( )に入る最も適切な語句を ① ~ ④から選びなさい。 (1) He went on speaking as if she ( 1 can't 2 hasn't ) there. Son 3 wouldn't ) by a dentist this morning. ult niles 3 checking wahiwon (青山学院大 ) ④weren't pomibinand (岩手医科大) 24 to check 2 checked (3) You should not keep any pets ( 1 after 2 unless ) you can take good care of them. 3 when (中央大) ④which 1 as 2 in ) all be correct. ②anytime (6) If the weather ( ①must have been (4) This town will change ( ) another ten years. (5) Those may not ( 1 absolute ) fine yesterday, I would have done the laundry. 2 is (7) Studying takes up a lot of my time during the week, ( ) little time for hobbies. (芝浦工業大) since 3 of (國學院大) 3 everything ④necessarily (関西学院大 ) ③ wasn't 4 had been (皇學館大) ①1 has left (8) Have you heard the rumors ( 1 that 2 what leaves leaving 4 left ) Susan has returned to this town? ③ which (麗澤大) ④ who 1 by (9) What was found in this experiment is ( 2 for (10)( ) what to say, she remained silent. ) great importance to researchers. 3 in (立命館大) 4 of (愛知工業大) 1 Not knowing 2 Being not knowing ③No knowing ④Knowing no (11) I tried to ( 1 have 2 make ) her to tell me what happened last night. 3 get (十文字学園女子大) 4 let How gimon and (12) Do what you like, as ( 1 far 2 much B in 1 in 2 with bnat am ) as you leave me alone. 3 long (13) This tool is dangerous. Please read the instructions ( (14) If I hadn't drunk so much last night, I ( 1 feel (15) I wish you 1 attend (16) If I ( 1 were ) 2 will feel ) the party yesterday. 2 were attending ) much better than I do right now. ③ would feel ③ have attended (中京大) 4 would have felt (目白大) ④had attended ) in your situation, I would be more careful about what you post on social media. (フェリス女学院大) 4 many ) care. (聖隷クリストファー大) at ④take gwol 3 will be (南山大) ④would be

多様体を構成するために、位相空間に完全アトラスを導入するところで質問です。 完全アトラスを導入するメリットとして、この文章の下線部を「異なる座標系を用いたのに同じ計算ができてしまうという問題が解消される」解釈したのですが、そこがよくわかりません。座標系を変えて計算する... 続きを読む

1 Two n-dimensional coordinate systems & and ŋ in S overlap smoothly provided the functions on¯¹ and ŋo §¯¹ are both smooth. Explicitly, if : U → R" and ŋ: R", then ŋ 1 is defined on the open set ε (ur) → ° (UV) V and carries it to n(u)—while its inverse function § 4-1 runs in the opposite direction (see Figure 1). These functions are then required to be smooth in the usual Euclidean sense defined above. This condition is con- sidered to hold trivially if u and do not meet. Č (UV) R" Ĕ(U) n(UV) R" S n(v) Figure 1. 1. Definition. An atlas A of dimension n on a space S is a collection of n-dimensional coordinate systems in S such that (A1) each point of S is contained in the domain of some coordinate system in, and (A2) any two coordinate systems in ✅ overlap smoothly. An atlas on S makes it possible to do calculus consistently on all of S. But different atlases may produce the same calculus, a technical difficulty eliminated as follows. Call an atlas Con S complete if C contains each co- ordinate system in S that overlaps smoothly with every coordinate system in C. 2. Lemma. Each atlas ✅ on S is contained in a unique complete atlas. Proof. If has dimension n, let A' be the set of all n-dimensional coordinate systems in S that overlap smoothly with every one contained in A. (a) A' is an atlas (of the same dimension as ✅).

問2.1の証明が分かりません。 ※1枚目が質問内容、2枚目が仮定

問 2.1 例1 (b), (c) で R" に定義された各種の距離 dp : R" × R” → [0,∞) (p = 1,2,...,∞) において, R” の点列 πm:= (x(m),x(m),...,xmm))∈R(m= R" 2 1,2,･･･) が, 点æ= (π1, 2,...,πn) ∈R" に収束するためには,各k ∈ {1, 2,...,n} に対し (m) →πk (m→8) となることが必要十分であることを示せ.

数学の行列について質問です 下の写真の問題の解き方がわかりません。教えていただけるとありがたいです。

23:37 Previous Problem Problem List Next Problem Consider a sequence (an) 20 defined by the following recurrence relation: n=0 21 ao = 1, a1 == -3, An+2 = 11an+1 18an (n ≥ 0). (1) Find a matrix A satisfying the following: A - [an+2] an+1 an+1 = An (2) Calculate the eigenvalues of the matrix A, where t1t2 (No partial credit). t₁ = = ったこ = (3) Find the eigenvectors of the matrix A. (i) The eigenvector with respect to the eigenvalue +1: V₁ = = t [ ], (ii) The eigenvector with respect to the eigenvalue t₂: v₂ = [ ]. (4) Diagonalize the matrix A, that is, calculate the following, where P = [v1_v2]. P-1 AP = (5) Calculate A" by using diagonalization. An 17

赤線を引いたところのbetter offのoffはどんな概念を有しているか、また品詞は何か？という問いがあるんですが、全く分からないので詳しく説明してくださいお願いします…

His parents were poor illegal immigrants from Mexico. Henry, because he was born in the United States, had U.S. citizenship. However, Henry's father had trouble with the law and was frequently in jail. His mother decided that they would be better off away from her husband and moved to New Mexico with her six children. Henry was four years old at the time. In their new surroundings, the family often had to share a living space with other poor families. Four children often slept in a single bed. Henry's mother worked hard at two jobs

英作文の添削をしてほしいです。文法的なところとか、スペルだけでもいいので、お願いします！何を書いているかわからなければ、言ってもらって全然大丈夫です！

4 POINTS TOPIC Agree or disagree: Japanese companies should require employees to use English in their workplace al ●Write an essay on the given TOPIC. Use TWO of the POINTS below to support your answer. Structure: introduction, main body, and conclusion Suggested length: 120-150 words 18 ●Write your essay in the space provided on Side B of your answer sheet. Any writing outside the space will not be graded. ■Communication barriers 言語の壁 LExpansion of market 市場の拡大 ●Labor shortage 人員不足 Stress b ストレス 日本語は難しい と言われている。 total:128 words 英語を使えば、日本語を話せないが、 日本で働きたい外国人の雇用につながる ―海外進出商品のに人知度叩かも、 ・海外のニーズに応じた 商品づくりもできる Galaxy A54.5Gの解しょう もし社員が英語を話せたら。 外国人の雇用につながる ・経済が

なぜこの文章はSV…がなく、to不定詞だけなんでしょうか 訳し方がわかりません

1 SPACE JUNK It is hard to believe that space itself can be polluted by human efforts), but 助(皮)Vi it is true even the outer limits can face damage. We have trashed the orbits our 副 助 Vt O spacecraft travel through. So much so that, before every launch of a space shuttle, NASA's high-speed computers run for a full 24 hours on just one element of the M... flight to choose a safe orbit, so that the shuttle will not be destroyed (by colliding) (Vi) M with some other man-made orbiting body) M 形 F!! 71% 形 ace is in fact