{"id":3441,"date":"2012-09-11T19:40:20","date_gmt":"2012-09-11T19:40:20","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=3441"},"modified":"2014-12-02T08:32:03","modified_gmt":"2014-12-02T08:32:03","slug":"determinant-of-a-matrix","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/09\/11\/determinant-of-a-matrix\/","title":{"rendered":"Determinant of a Matrix"},"content":{"rendered":"

Every square matrix is associated with a real number which is called the determinant<\/em> of the square matrix. Let S<\/em><\/strong> be the set of all square matrices and R<\/em><\/strong> be the set of real numbers. Then the function f:S->R is called the determinant. The determinant of a matrix M<\/em><\/strong> is denoted by |M| <\/em><\/strong>or detM<\/em><\/strong>. It can be computed using a specific mathematical operation on the elements of the matrix.<\/p>\n

The determinant of a matrix is used to solve the system of equations. Also, the determinant of a matrix gives an important information when the elements of a matrix are associated with a linear transformation.<\/p>\n

Determinant of a 2×2 matrix:<\/h4>\n

The determinant of a 2×2 matrix\u00a0\"\"<\/a> is defined as ad-bc. It is nothing but the difference of cross products of the elements in order.<\/p>\n

Example:<\/strong><\/p>\n

The determinant of \"\"<\/a>\u00a0is 2*2 \u2013(3*-1)=4+3=7.<\/p>\n

Minor and Co-factor of an element:<\/h4>\n

Minor of an element of a 3×3 matrix is the determinant of 2×2 matrix obtained after leaving the row and column containing it.<\/p>\n

The cofactor of an element is the product of its minor with (-1)i+j<\/sup> where i<\/em><\/strong> is the row number and j<\/em><\/strong> is the column number containing it.<\/p>\n

Example:<\/strong><\/p>\n

Let A =\"\"<\/a><\/p>\n

Minor of 1 =\"\"<\/a> =-5+8=3; Co-factor of 1 = (-1)1+1<\/sup> 3 = 3<\/p>\n

Minor of 4 =\"\"<\/a> =-2-4 =-6.; Co-factor of 4 = (-1)1+2<\/sup> (-6) =(-1)(-6)=6<\/p>\n

Determinant of a 3×3 matrix:<\/h4>\n

The determinant of a 3×3 matrix is the sum of the products of elements of any row (or column) with their corresponding cofactors.<\/p>\n

Example:<\/strong><\/p>\n

Let A =\"\"<\/a><\/p>\n

Its corresponding cofactor matrix is \"\"<\/a><\/p>\n

So, if we use the first row to find the determinant, taking the sum of the products of first row elements with the corresponding elements of the co-factor matrix then,<\/p>\n

|A| = 1*3 + 4*6 + (-2)*9 = 3 +24-18 = 9
\n<\/strong><\/p>\n

 <\/p>\n

Still need help with Mathematics? Please read more about our Mathematics tutoring services<\/a>.
\nSchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Patterson visit: Tutoring in Patterson.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Every square matrix is associated with a real number which is called the determinant of the square matrix. Let S be the set of all square matrices and R be the set of real numbers. Then the function f:S->R is called the determinant. The determinant of a matrix M is denoted by |M| or detM. […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[305,483,1123,1396,1774],"class_list":["post-3441","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-cofactor","tag-determinant","tag-minor","tag-product","tag-sum"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/3441","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=3441"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/3441\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=3441"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=3441"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=3441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}