When multiplying a 3×1 matrix and a 1×3 matrix the resultant matrix is a Group of answer choices 1×1 1×3 3×3 3×1<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To understand the result of multiplying a 3\u00d71<\/strong> matrix and a 1\u00d73<\/strong> matrix, we must look at the rules of matrix multiplication<\/strong>.<\/p>\n\n\n\n Let\u2019s define two matrices:<\/p>\n\n\n\n Matrix multiplication is defined only when the number of columns in the first matrix equals the number of rows in the second matrix<\/strong>. For these two matrices:<\/p>\n\n\n\n Since the inner dimensions match (1 = 1), we can multiply them.<\/p>\n\n\n\n The resulting matrix has the dimensions of the outer numbers<\/strong>:<\/p>\n\n\n\n A=[246],B=[135]A = \\begin{bmatrix} 2 \\\\ 4 \\\\ 6 \\end{bmatrix}, \\quad B = \\begin{bmatrix} 1 & 3 & 5 \\end{bmatrix} AB=[2\u22c512\u22c532\u22c554\u22c514\u22c534\u22c556\u22c516\u22c536\u22c55]=[26104122061830]AB = \\begin{bmatrix} 2 \\cdot 1 & 2 \\cdot 3 & 2 \\cdot 5 \\\\ 4 \\cdot 1 & 4 \\cdot 3 & 4 \\cdot 5 \\\\ 6 \\cdot 1 & 6 \\cdot 3 & 6 \\cdot 5 \\end{bmatrix} = \\begin{bmatrix} 2 & 6 & 10 \\\\ 4 & 12 & 20 \\\\ 6 & 18 & 30 \\end{bmatrix}<\/p>\n\n\n\n So, the resulting matrix is 3\u00d73<\/strong>.<\/p>\n\n\n\n This is known as the outer product<\/strong> of two vectors. A column vector (3\u00d71) and a row vector (1\u00d73) produce a square matrix where each element is the product of the respective elements from A and B. This concept is widely used in linear algebra, machine learning, and physics.<\/p>\n","protected":false},"excerpt":{"rendered":" When multiplying a 3×1 matrix and a 1×3 matrix the resultant matrix is a Group of answer choices 1×1 1×3 3×3 3×1 The correct answer and explanation is: Correct Answer: 3×3 Explanation: To understand the result of multiplying a 3\u00d71 matrix and a 1\u00d73 matrix, we must look at the rules of matrix multiplication. Matrix […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18279","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18279","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18279"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18279\/revisions"}],"predecessor-version":[{"id":18280,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18279\/revisions\/18280"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Correct Answer: 3×3<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation:<\/h3>\n\n\n\n
Matrix Dimensions:<\/h4>\n\n\n\n
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Example: A=[a1a2a3]A = \\begin{bmatrix} a_1 \\\\ a_2 \\\\ a_3 \\end{bmatrix}<\/li>\n\n\n\n
Example: B=[b1b2b3]B = \\begin{bmatrix} b_1 & b_2 & b_3 \\end{bmatrix}<\/li>\n<\/ul>\n\n\n\nMatrix Multiplication Rule:<\/h4>\n\n\n\n
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Resulting Dimensions:<\/h4>\n\n\n\n
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Example:<\/h4>\n\n\n\n