{"id":19985,"date":"2024-04-15T05:46:51","date_gmt":"2024-04-15T05:46:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=19985"},"modified":"2024-04-15T05:46:51","modified_gmt":"2024-04-15T05:46:51","slug":"if-texta-left-beginarray20c-15-62-endarray-right-and-textb-left-beginarray20c-37-84-endarray-righttexta","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-texta-left-beginarray20c-15-62-endarray-right-and-textb-left-beginarray20c-37-84-endarray-righttexta\/","title":{"rendered":"If \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} 1&5 \\\\ 6&2 \\end{array}} \\right]\\] and \\[{\\text{B}} = \\left[ {\\begin{array}{*{20}{c}} 3&7 \\\\ 8&4 \\end{array}} \\right],\\,{\\text{A}}{{\\text{B}}^{\\text{T}}}\\] is equal to A. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\\\ {32}&{56} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 3&{40} \\\\ {42}&8 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} {43}&{27} \\\\ {34}&{50} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{32} \\\\ {28}&{56} \\end{array}} \\right]\\]"},"content":{"rendered":"

[amp_mcq option1=”\\[\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\\\ {32}&{56} \\end{array}} \\right]\\]” option2=”\\[\\left[ {\\begin{array}{*{20}{c}} 3&{40} \\\\ {42}&8 \\end{array}} \\right]\\]” option3=”\\[\\left[ {\\begin{array}{*{20}{c}} {43}&{27} \\\\ {34}&{50} \\end{array}} \\right]\\]” option4=”\\[\\left[ {\\begin{array}{*{20}{c}} {38}&{32} \\\\ {28}&{56} \\end{array}} \\right]\\]” correct=”option1″]<\/p>\n

The correct answer is $\\boxed{\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\ {32}&{56} \\end{array}} \\right]}$.<\/p>\n

To find the product of two matrices, we can use the following formula:<\/p>\n

$$(A \\times B){ij} = \\sum<\/em>{k=1}^n A_{ik} B_{kj}$$<\/p>\n

where $A$ is an $m \\times n$ matrix, $B$ is an $n \\times p$ matrix, and $(A \\times B)_{ij}$ is the element in the $i$th row and $j$th column of the product matrix.<\/p>\n

In this case, $A$ is a 2 $\\times$ 2 matrix and $B$ is a 2 $\\times$ 2 matrix. Therefore, the product matrix will be a 2 $\\times$ 2 matrix.<\/p>\n

To find the element in the first row and first column of the product matrix, we multiply the first row of $A$ with the first column of $B$ and add the products together. This gives us:<\/p>\n

$$(A \\times B)_{11} = 1 \\cdot 3 + 5 \\cdot 8 = 38$$<\/p>\n

To find the element in the second row and first column of the product matrix, we multiply the second row of $A$ with the first column of $B$ and add the products together. This gives us:<\/p>\n

$$(A \\times B)_{21} = 6 \\cdot 3 + 2 \\cdot 8 = 32$$<\/p>\n

To find the element in the first row and second column of the product matrix, we multiply the first row of $A$ with the second column of $B$ and add the products together. This gives us:<\/p>\n

$$(A \\times B)_{12} = 1 \\cdot 7 + 5 \\cdot 4 = 28$$<\/p>\n

To find the element in the second row and second column of the product matrix, we multiply the second row of $A$ with the second column of $B$ and add the products together. This gives us:<\/p>\n

$$(A \\times B)_{22} = 6 \\cdot 7 + 2 \\cdot 4 = 56$$<\/p>\n

Therefore, the product matrix is:<\/p>\n

$$(A \\times B) = \\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\ {32}&{56} \\end{array}} \\right]$$<\/p>\n","protected":false},"excerpt":{"rendered":"

[amp_mcq option1=”\\[\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\\\ {32}&{56} \\end{array}} \\right]\\]” option2=”\\[\\left[ {\\begin{array}{*{20}{c}} 3&{40} \\\\ {42}&8 \\end{array}} \\right]\\]” option3=”\\[\\left[ {\\begin{array}{*{20}{c}} {43}&{27} \\\\ {34}&{50} \\end{array}} \\right]\\]” option4=”\\[\\left[ {\\begin{array}{*{20}{c}} {38}&{32} \\\\ {28}&{56} \\end{array}} \\right]\\]” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[489],"tags":[],"class_list":["post-19985","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","no-featured-image-padding"],"yoast_head":"\nIf \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} 1&5 \\\\ 6&2 \\end{array}} \\right]\\] and \\[{\\text{B}} = \\left[ {\\begin{array}{*{20}{c}} 3&7 \\\\ 8&4 \\end{array}} \\right],\\,{\\text{A}}{{\\text{B}}^{\\text{T}}}\\] is equal to A. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\\\ {32}&{56} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 3&{40} \\\\ {42}&8 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} {43}&{27} \\\\ {34}&{50} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{32} \\\\ {28}&{56} \\end{array}} \\right]\\]<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-texta-left-beginarray20c-15-62-endarray-right-and-textb-left-beginarray20c-37-84-endarray-righttexta\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} 1&5 \\\\ 6&2 \\end{array}} \\right]\\] and \\[{\\text{B}} = \\left[ {\\begin{array}{*{20}{c}} 3&7 \\\\ 8&4 \\end{array}} \\right],\\,{\\text{A}}{{\\text{B}}^{\\text{T}}}\\] is equal to A. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\\\ {32}&{56} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 3&{40} \\\\ {42}&8 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} {43}&{27} \\\\ {34}&{50} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{32} \\\\ {28}&{56} \\end{array}} \\right]\\]\" \/>\n<meta property=\"og:description\" content=\"[amp_mcq option1=”[left[ {begin{array}{*{20}{c}} {38}&{28} \\ {32}&{56} end{array}} right]]” option2=”[left[ {begin{array}{*{20}{c}} 3&{40} \\ {42}&8 end{array}} right]]” option3=”[left[ {begin{array}{*{20}{c}} {43}&{27} \\ {34}&{50} end{array}} right]]” option4=”[left[ {begin{array}{*{20}{c}} {38}&{32} \\ {28}&{56} end{array}} right]]” correct=”option1″]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-texta-left-beginarray20c-15-62-endarray-right-and-textb-left-beginarray20c-37-84-endarray-righttexta\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-15T05:46:51+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"If \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} 1&5 \\\\ 6&2 \\end{array}} \\right]\\] and \\[{\\text{B}} = \\left[ {\\begin{array}{*{20}{c}} 3&7 \\\\ 8&4 \\end{array}} \\right],\\,{\\text{A}}{{\\text{B}}^{\\text{T}}}\\] is equal to A. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\\\ {32}&{56} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 3&{40} \\\\ {42}&8 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} {43}&{27} \\\\ {34}&{50} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{32} \\\\ {28}&{56} \\end{array}} \\right]\\]","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/if-texta-left-beginarray20c-15-62-endarray-right-and-textb-left-beginarray20c-37-84-endarray-righttexta\/","og_locale":"en_US","og_type":"article","og_title":"If \\[{\\text{A}} = \\left[ {\\begin{array}{*{20}{c}} 1&5 \\\\ 6&2 \\end{array}} \\right]\\] and \\[{\\text{B}} = \\left[ {\\begin{array}{*{20}{c}} 3&7 \\\\ 8&4 \\end{array}} \\right],\\,{\\text{A}}{{\\text{B}}^{\\text{T}}}\\] is equal to A. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{28} \\\\ {32}&{56} \\end{array}} \\right]\\] B. \\[\\left[ {\\begin{array}{*{20}{c}} 3&{40} \\\\ {42}&8 \\end{array}} \\right]\\] C. \\[\\left[ {\\begin{array}{*{20}{c}} {43}&{27} \\\\ {34}&{50} \\end{array}} \\right]\\] D. \\[\\left[ {\\begin{array}{*{20}{c}} {38}&{32} \\\\ {28}&{56} \\end{array}} \\right]\\]","og_description":"[amp_mcq option1=”[left[ {begin{array}{*{20}{c}} {38}&{28} \\ {32}&{56} end{array}} right]]” option2=”[left[ {begin{array}{*{20}{c}} 3&{40} \\ {42}&8 end{array}} right]]” option3=”[left[ {begin{array}{*{20}{c}} {43}&{27} \\ {34}&{50} end{array}} right]]” option4=”[left[ {begin{array}{*{20}{c}} {38}&{32} \\ {28}&{56} end{array}} right]]” correct=”option1″]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-texta-left-beginarray20c-15-62-endarray-right-and-textb-left-beginarray20c-37-84-endarray-righttexta\/","og_site_name":"MCQ and Quiz for 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