{"id":6716,"date":"2014-03-06T16:36:17","date_gmt":"2014-03-06T16:36:17","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6716"},"modified":"2014-12-02T08:25:31","modified_gmt":"2014-12-02T08:25:31","slug":"math-review-of-operations-with-matrices","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/03\/06\/math-review-of-operations-with-matrices\/","title":{"rendered":"Math Review of Operations with Matrices"},"content":{"rendered":"

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

Matrices, like other numbers, variables, and expressions, can be involved in mathematical operations.\u00a0 The rules are different, as every element of each matrix must be included.\u00a0 Also, only certain types of matrices can be combined.<\/p>\n

How Are Matrices Added?<\/strong><\/p>\n

In order to add matrices, both matrices must be of the same dimensions so that corresponding elements can be added. Suppose the matrices to be added\u00a0were [1 2 3 4]\u00a0\u00a0and [5 6 7 8].\u00a0 In order to add them, each corresponding element would be added, as 1 + 5,\u00a02 + 6, 3 + 7, 4 + 8\u00a0or [6 8 10 12].<\/p>\n

How Are Matrices Moved?<\/strong><\/p>\n

A matrix can describe the coordinates of a geometric figure as it is drawn on a plane.\u00a0 Suppose triangle \u2206ABC has point A at (3, 2), point B at (-3, 0), and point C at (2, -5).\u00a0 A matrix that represents its dimensions would be [3 -3 2 2 0 -5].\u00a0 If the triangle were moved, or translated, so that it has the same size, shape and direction, 2 units to the right and 2 units down, it would be the same as adding the matrices [3 -3 2 2 0 -5]\u00a0and [2 2 2 -2 -2 -2]\u00a0.\u00a0 Using the rule for adding matrices, the new matrix would be[3+2\u00a0-3+2\u00a0 2+2\u00a0 2-2\u00a0 0-2 -5-2]\u00a0\u00a0or [5 -1 4 0 -2 -7].<\/p>\n

How Are Matrices Enlarged?<\/strong><\/p>\n

Matrices are enlarged by multiplying each element of the original matrix by the same number.\u00a0 Suppose triangle ABC, with matrix [3 -3 2 2 0 -5]\u00a0were to be enlarged so that its perimeter were twice its size. Each element is multiplied by 2, as in 2[3 -3 2 2 0 -5].\u00a0 The new matrix would be [6 -6 4 4 0 -10].<\/p>\n

What Is a Determinant?<\/strong><\/p>\n

A determinant is associated with its square matrix.\u00a0 It can be solved as a single number.\u00a0 Cramer’s rule for evaluating the determinant of a 2 X 2 matrix starts with the matrix itself.\u00a0 Suppose the matrix were [1 2 3 4].\u00a0Its determinant would be found by multiplying the 1st and 4th elements (or 1 \u2219 4) and subtracting the product of the 2nd and 3rd elements (2 \u2219 3).\u00a0 In this case, 4 – 6 = -2.<\/p>\n

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Overview: Matrices, like other numbers, variables, and expressions, can be involved in mathematical operations.\u00a0 The rules are different, as every element of each matrix must be included.\u00a0 Also, only certain types of matrices can be combined. How Are Matrices Added? In order to add matrices, both matrices must be of the same dimensions so that […]<\/p>\n","protected":false},"author":22,"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":[2603,2605,2606,2604],"class_list":["post-6716","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-adding-matrices","tag-cramers-rule","tag-enlarging-matrices","tag-moving-matrices"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6716","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6716"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6716\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}