{"id":991,"date":"2025-10-31T01:28:46","date_gmt":"2025-10-31T01:28:46","guid":{"rendered":"https:\/\/ykim.synology.me\/wordpress\/?p=991"},"modified":"2025-10-31T14:49:33","modified_gmt":"2025-10-31T14:49:33","slug":"derivation_of_cramers_rule","status":"publish","type":"post","link":"https:\/\/ykim.synology.me\/wordpress\/derivation_of_cramers_rule-991\/","title":{"rendered":"Derivation of Cramer’s Rule"},"content":{"rendered":"\n

\ud06c\ub77c\uba54\ub974 \uacf5\uc2dd(Cramer’s Rule)\uc744 \uc720\ub3c4\ud574 \ubd05\uc2dc\ub2e4. \uace0\ub4f1\ud559\uc0dd\uc5d0\uac8c \uac00\uc7a5 \uc775\uc219\ud55c ‘\uac00\uac10\ubc95'(\uc18c\uac70\ubc95)\uc744 \uc0ac\uc6a9\ud574\uc11c 2×2 \uc5f0\ub9bd \ubc29\uc815\uc2dd\uc744 \ud478\ub294 \uacfc\uc815\uc5d0\uc11c \uc774 \uacf5\uc2dd\uc774 \uc5b4\ub5bb\uac8c \ub098\uc624\ub294\uc9c0 \ubcf4\uc5ec\ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n

\ub2e4\uc74c\uacfc \uac19\uc740 \uc77c\ubc18\uc801\uc778 \uc5f0\ub9bd \ubc29\uc815\uc2dd\uc774 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large \\begin{cases} ax + by = e \\\\ cx + dy = f \\end{cases}[\/katex]<\/p>\n\n\n\n

\n\n\n\n

1\ub2e8\uacc4: $y$\ub97c \uc18c\uac70\ud558\uc5ec $x$ \uad6c\ud558\uae30<\/h3>\n\n\n\n

\uba3c\uc800, [katex]\\Large y[\/katex]\ud56d\uc744 \uc5c6\uc560\uae30 \uc704\ud574 \ub450 \uc2dd\uc744 \uc870\uc791\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n

\uccab \ubc88\uc9f8 \uc2dd\uc758 \uc591\ubcc0\uc5d0 [katex]\\Large d[\/katex]\ub97c \uacf1\ud558\uace0, \ub450 \ubc88\uc9f8 \uc2dd\uc758 \uc591\ubcc0\uc5d0 [katex]\\Large b[\/katex]\ub97c \uacf1\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large \\begin{cases} (ad)x + (bd)y = ed \\\\ (bc)x + (bd)y = fb \\end{cases}[\/katex]<\/p>\n\n\n\n

\uc774\uc81c \uccab \ubc88\uc9f8 \uc2dd\uc5d0\uc11c \ub450 \ubc88\uc9f8 \uc2dd\uc744 \ube8d\ub2c8\ub2e4. [katex]\\Large y[\/katex]\ud56d\uc774 \uc0ac\ub77c\uc9d1\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large (ad)x – (bc)x = ed – fb[\/katex]<\/p>\n\n\n\n

[katex]\\Large x[\/katex]\ub85c \ubb36\uc5b4\uc90d\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large (ad – bc)x = ed – fb[\/katex]<\/p>\n\n\n\n

[katex]\\Large ad – bc[\/katex]\uac00 0\uc774 \uc544\ub2c8\ub77c\uace0 \uac00\uc815\ud558\uace0 \uc591\ubcc0\uc744 \ub098\ub204\uba74 [katex]\\Large x[\/katex]\uc758 \ud574\ub97c \uc5bb\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large x = \\frac{ed – fb}{ad – bc}[\/katex]<\/p>\n\n\n\n

\n\n\n\n

2\ub2e8\uacc4: x\ub97c \uc18c\uac70\ud558\uc5ec \u315b \uad6c\ud558\uae30<\/h3>\n\n\n\n

\uc774\ubc88\uc5d0\ub294 [katex]\\Large x[\/katex]\ud56d\uc744 \uc5c6\uc560\uae30 \uc704\ud574 \uc6d0\ub798\uc758 \ub450 \uc2dd\uc73c\ub85c \ub3cc\uc544\uac11\ub2c8\ub2e4.<\/p>\n\n\n\n

\uccab \ubc88\uc9f8 \uc2dd\uc758 \uc591\ubcc0\uc5d0 [katex]\\Large c[\/katex]\ub97c \uacf1\ud558\uace0, \ub450 \ubc88\uc9f8 \uc2dd\uc758 \uc591\ubcc0\uc5d0 [katex]\\Large a[\/katex]\ub97c \uacf1\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large \\begin{cases} (ac)x + (bc)y = ec \\\\ (ac)x + (ad)y = fa \\end{cases}[\/katex]<\/p>\n\n\n\n

\uc774\uc81c \ub450 \ubc88\uc9f8 \uc2dd\uc5d0\uc11c \uccab \ubc88\uc9f8 \uc2dd\uc744 \ube8d\ub2c8\ub2e4. [katex]\\Large x[\/katex]\ud56d\uc774 \uc0ac\ub77c\uc9d1\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large (ad)y – (bc)y = fa – ec[\/katex]<\/p>\n\n\n\n

[katex]\\Large y[\/katex]\ub85c \ubb36\uc5b4\uc90d\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large (ad – bc)y = af – ec[\/katex]<\/p>\n\n\n\n

\uc591\ubcc0\uc744 [katex]\\Large ad – bc[\/katex]\ub85c \ub098\ub204\uba74 [katex]\\Large y[\/katex]\uc758 \ud574\ub97c \uc5bb\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large y = \\frac{af – ec}{ad – bc}[\/katex]<\/p>\n\n\n\n

\n\n\n\n

3\ub2e8\uacc4: \uacb0\uacfc\ub97c \ud589\ub82c\uc2dd(Determinant)\uacfc \uc5f0\uacb0\ud558\uae30<\/h3>\n\n\n\n

\uc774\uc81c \uc6b0\ub9ac\uac00 \uad6c\ud55c \ud574\uac00 \ud589\ub82c\uc2dd\uacfc \uc5b4\ub5a4 \uad00\uacc4\uac00 \uc788\ub294\uc9c0 \uc0b4\ud3b4\ubd05\uc2dc\ub2e4.<\/p>\n\n\n\n

\ubd84\ubaa8(Denominator):<\/p>\n\n\n\n

[katex]\\Large x[\/katex]\uc640 [katex]\\Large y[\/katex]\uc758 \ud574\ub294 \ubaa8\ub450 [katex]\\Large ad – bc[\/katex]\ub77c\ub294 \uacf5\ud1b5\ub41c \ubd84\ubaa8\ub97c \uac00\uc9d1\ub2c8\ub2e4.<\/p>\n\n\n\n

\uc774 \uac12\uc740 \uc6d0\ub798 \ubc29\uc815\uc2dd\uc758 \uacc4\uc218\ub4e4\ub85c \ub9cc\ub4e0 \ud589\ub82c [katex]\\Large A[\/katex]\uc758 \ud589\ub82c\uc2dd(determinant)\uacfc \uc815\ud655\ud788 \uac19\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large A = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}[\/katex]<\/p>\n\n\n\n

[katex display=true]\\Large \\det(A) = ad – bc[\/katex]<\/p>\n\n\n\n

\ubd84\uc790(Numerator):<\/strong><\/p>\n\n\n\n

1. [katex]\\Large x[\/katex]\uc758 \ubd84\uc790: [katex]\\Large ed – fb[\/katex]<\/p>\n\n\n\n

\uc774 \uac12\uc740, \uc6d0\ub798 \ud589\ub82c [katex]\\Large A[\/katex]\uc758 **\uccab \ubc88\uc9f8 \uc5f4([katex]\\Large x[\/katex] \uacc4\uc218 \uc5f4)**\uc744 \uc0c1\uc218 \ubca1\ud130 [katex]\\Large \\begin{pmatrix} e \\ f \\end{pmatrix}[\/katex]\ub85c \ubc14\uafbc \uc0c8\ub85c\uc6b4 \ud589\ub82c\uc758 \ud589\ub82c\uc2dd\uacfc \uac19\uc2b5\ub2c8\ub2e4. \uc774 \ud589\ub82c\uc744 [katex]\\Large A_x[\/katex]\ub77c\uace0 \ubd80\ub985\uc2dc\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large A_x = \\begin{pmatrix} e & b \\\\ f & d \\end{pmatrix}[\/katex]<\/p>\n\n\n\n

[katex display=true]\\Large \\det(A_x) = ed – bf[\/katex]<\/p>\n\n\n\n

2. [katex]\\Large y[\/katex]\uc758 \ubd84\uc790: [katex]\\Large af – ec[\/katex]<\/p>\n\n\n\n

\uc774 \uac12\uc740, \uc6d0\ub798 \ud589\ub82c [katex]\\Large A[\/katex]\uc758 **\ub450 \ubc88\uc9f8 \uc5f4([katex]\\Large y[\/katex] \uacc4\uc218 \uc5f4)**\uc744 \uc0c1\uc218 \ubca1\ud130 [katex]\\Large \\begin{pmatrix} e \\ f \\end{pmatrix}[\/katex]\ub85c \ubc14\uafbc \ud589\ub82c [katex]\\Large A_y[\/katex]\uc758 \ud589\ub82c\uc2dd\uacfc \uac19\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large A_y = \\begin{pmatrix} a & e \\\\ c & f \\end{pmatrix}[\/katex]<\/p>\n\n\n\n

[katex display=true]\\Large \\det(A_y) = af – ec[\/katex]<\/p>\n\n\n\n

\n\n\n\n

4\ub2e8\uacc4: \ud06c\ub77c\uba54\ub974 \uacf5\uc2dd \uc644\uc131<\/h3>\n\n\n\n

\uc774 \uad00\uacc4\ub97c \ubaa8\ub450 \uc885\ud569\ud558\uba74, [katex]\\Large x[\/katex]\uc640 [katex]\\Large y[\/katex]\uc758 \ud574\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uae54\ub054\ud55c \ud589\ub82c\uc2dd\uc758 \ube44\uc728\ub85c \ud45c\ud604\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n

[katex display=true]\\Large x = \\frac{ed – fb}{ad – bc} = \\frac{\\det(A_x)}{\\det(A)}[\/katex]<\/p>\n\n\n\n

[katex display=true]\\Large y = \\frac{af – ec}{ad – bc} = \\frac{\\det(A_y)}{\\det(A)}[\/katex]<\/p>\n\n\n\n

\uc774\uac83\uc774 \ubc14\ub85c \ud06c\ub77c\uba54\ub974 \uacf5\uc2dd\uc785\ub2c8\ub2e4.<\/p>\n

<\/div>
<\/div>","protected":false},"excerpt":{"rendered":"

\ud06c\ub77c\uba54\ub974 \uacf5\uc2dd(Cramer’s Rule)\uc744 \uc720\ub3c4\ud574 \ubd05\uc2dc\ub2e4. \uace0\ub4f1\ud559\uc0dd\uc5d0\uac8c \uac00\uc7a5 \uc775\uc219\ud55c ‘\uac00\uac10\ubc95'(\uc18c\uac70\ubc95)\uc744 \uc0ac\uc6a9\ud574\uc11c 2×2 \uc5f0\ub9bd \ubc29\uc815\uc2dd\uc744 \ud478\ub294 \uacfc\uc815\uc5d0\uc11c \uc774 \uacf5\uc2dd\uc774 \uc5b4\ub5bb\uac8c \ub098\uc624\ub294\uc9c0 \ubcf4\uc5ec\ub4dc\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. \ub2e4\uc74c\uacfc \uac19\uc740 \uc77c\ubc18\uc801\uc778 \uc5f0\ub9bd \ubc29\uc815\uc2dd\uc774 \uc788\uc2b5\ub2c8\ub2e4. [katex display=true]\\Large \\begin{cases} ax + by = e \\\\ cx + dy = f \\end{cases}[\/katex] 1\ub2e8\uacc4: $y$\ub97c \uc18c\uac70\ud558\uc5ec $x$ \uad6c\ud558\uae30 \uba3c\uc800, [katex]\\Large y[\/katex]\ud56d\uc744 \uc5c6\uc560\uae30 \uc704\ud574 \ub450 \uc2dd\uc744 \uc870\uc791\ud569\ub2c8\ub2e4. \uccab…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_kadence_starter_templates_imported_post":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","yasr_overall_rating":0,"yasr_post_is_review":"","yasr_auto_insert_disabled":"","yasr_review_type":"","fifu_image_url":"","fifu_image_alt":"","iawp_total_views":0,"footnotes":""},"categories":[69],"tags":[],"class_list":["post-991","post","type-post","status-publish","format-standard","hentry","category-education-slug"],"yasr_visitor_votes":{"stars_attributes":{"read_only":false,"span_bottom":false},"number_of_votes":0,"sum_votes":0},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/991","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/comments?post=991"}],"version-history":[{"count":11,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/991\/revisions"}],"predecessor-version":[{"id":1018,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/posts\/991\/revisions\/1018"}],"wp:attachment":[{"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/media?parent=991"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/categories?post=991"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ykim.synology.me\/wordpress\/wp-json\/wp\/v2\/tags?post=991"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}