# Linear Algebra/Partitioned Matrices

The matrix $P$ can be partitioned into 4 2×2 blocks
$P={\begin{bmatrix}1&1&2&2\\1&1&2&2\\3&3&4&4\\3&3&4&4\end{bmatrix}}$ $P_{11}={\begin{bmatrix}1&1\\1&1\end{bmatrix}},P_{12}={\begin{bmatrix}2&2\\2&2\end{bmatrix}},P_{21}={\begin{bmatrix}3&3\\3&3\end{bmatrix}},P_{22}={\begin{bmatrix}4&4\\4&4\end{bmatrix}}$ $P_{\text{partitioned}}={\begin{bmatrix}P_{11}&P_{12}\\P_{21}&P_{22}\end{bmatrix}}$
{"ft_lang_label":"__label__en","ft_lang_prob":0.92193484,"math_prob":0.99995446,"size":292,"snap":"2021-04-2021-17","text_gpt3_token_len":63,"char_repetition_ratio":0.22569445,"word_repetition_ratio":0.0,"special_character_ratio":0.1780822,"punctuation_ratio":0.02,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9958017,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,8,null,8,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-26T16:27:51Z\",\"WARC-Record-ID\":\"<urn:uuid:1060e72e-4644-4427-ae78-bdedde719562>\",\"Content-Length\":\"35388\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7976507a-d6e9-45a4-8162-6462998bed5f>\",\"WARC-Concurrent-To\":\"<urn:uuid:5dcd6e10-5716-4642-a4d5-3e45cdfa54e9>\",\"WARC-IP-Address\":\"208.80.154.224\",\"WARC-Target-URI\":\"https://en.wikibooks.org/wiki/Linear_Algebra/Partitioned_Matrices\",\"WARC-Payload-Digest\":\"sha1:2WDLY3TIFKIRUYJV2CODLY2DMR5554UW\",\"WARC-Block-Digest\":\"sha1:P6OMPDE5I3OVZWF5H7ITKNXUQMEBUQO7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610704800238.80_warc_CC-MAIN-20210126135838-20210126165838-00006.warc.gz\"}"}