# Monthly Archives: January 2014

## Completing Chapter 2 of Linear Algebra and Its Applications

Yesterday I posted the final worked-out solution for the exercises from chapter 2 of  Gilbert Strang’s Linear Algebra and Its Applications, Third Edition. My first post for chapter 2 was for exercise 2.1.1 almost exactly 29 months ago. This is … Continue reading

Posted in linear algebra | 2 Comments

## Linear Algebra and Its Applications, Review Exercise 2.33

Review exercise 2.33. Consider the following factorization: a) What is the rank of ? b) Find a basis for the row space of . c) Are rows 1, 2, and 3 of linearly independent: true or false? d) Find a … Continue reading

## Linear Algebra and Its Applications, Review Exercise 2.32

Review exercise 2.32. a) Find the subspace of such that for any vector in the subspace we have . b) Find a matrix for which this subspace is the nullspace. c) Find a matrix for which this subspace is the … Continue reading

Posted in linear algebra | Tagged , , | 2 Comments

## Linear Algebra and Its Applications, Review Exercise 2.31

Review exercise 2.31. Consider the rank-one matrix . Under what conditions would ? Answer: In order for to exist must be a square matrix; otherwise we could not multiply by since the number of columns of the first matrix would … Continue reading

## Linear Algebra and Its Applications, Review Exercise 2.30

Review exercise 2.30. Suppose that the matrix is a square matrix. a) Show that the nullspace of contains the nullspace of . b) Show that the column space of contains the column space of . Answer: a) Suppose is in … Continue reading

## Linear Algebra and Its Applications, Review Exercise 2.29

Review exercise 2.29. The following matrices represent linear transformations in the – plane with and as a basis. Describe the effect of each transformation. Answer: When the matrix is applied to the vector we obtain When the matrix is applied … Continue reading
{"ft_lang_label":"__label__en","ft_lang_prob":0.91341466,"math_prob":0.63823456,"size":3771,"snap":"2023-14-2023-23","text_gpt3_token_len":1014,"char_repetition_ratio":0.15078312,"word_repetition_ratio":0.14781298,"special_character_ratio":0.29116946,"punctuation_ratio":0.11747851,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9827564,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-28T15:09:38Z\",\"WARC-Record-ID\":\"<urn:uuid:be92a3f8-5c45-4b73-9cdc-1b2a939b9410>\",\"Content-Length\":\"69013\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:da3e1df9-4aee-4458-ace3-c8979a8746f5>\",\"WARC-Concurrent-To\":\"<urn:uuid:2a3bc6d0-327c-4836-ae1a-1631b2d31dd3>\",\"WARC-IP-Address\":\"192.0.78.13\",\"WARC-Target-URI\":\"https://math.hecker.org/2014/01/\",\"WARC-Payload-Digest\":\"sha1:7GFHISCSDCJDB3W7YQP7U3EFR3JIPW4P\",\"WARC-Block-Digest\":\"sha1:YTPYLOCARZL32WTGC4TKTNKHALNNEEQF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948867.32_warc_CC-MAIN-20230328135732-20230328165732-00753.warc.gz\"}"}