{"id":18762,"date":"2020-01-08T11:52:13","date_gmt":"2020-01-08T06:22:13","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=18762"},"modified":"2021-07-02T15:30:39","modified_gmt":"2021-07-02T10:00:39","slug":"2nd-puc-maths-question-bank-chapter-4-ex-4-4","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/2nd-puc-maths-question-bank-chapter-4-ex-4-4\/","title":{"rendered":"2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.4"},"content":{"rendered":"

Students can Download Maths Chapter 4 Determinants Ex 4.4 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.4<\/h2>\n

2nd PUC Maths Determinants NCERT Text Book Questions and Answers Ex 4.4<\/h3>\n

Write the minors and co-factors of the elements of following determinants<\/p>\n

Question 1.
\n(i)
\n\\(\\left|\\begin{array}{cc}{2} & {-4} \\\\{0} & {3}\\end{array}\\right|\\)
\nAnswer:
\n\"2nd<\/p>\n

(ii)
\n\\(\\left|\\begin{array}{ll}{a} & {c} \\\\{b} & {d}\\end{array}\\right|\\)
\nAnswer:
\n\"2nd
\n\"2nd<\/p>\n

\"KSEEB<\/p>\n

Question 2
\n(i)
\n\\(\\left|\\begin{array}{lll}{\\mathbf{1}} & {\\mathbf{0}} & {\\mathbf{0}} \\\\{\\mathbf{0}} & {\\mathbf{1}} & {\\mathbf{0}} \\\\{\\mathbf{0}} & {\\mathbf{0}} & {\\mathbf{1}}\\end{array}\\right|\\)
\nAnswer:
\n\"2nd<\/p>\n

(ii)
\n\\(\\left|\\begin{array}{ccc}{1} & {0} & {4} \\\\{3} & {5} & {-1} \\\\{0} & {1} & {2}\\end{array}\\right|\\)
\nAnswer:
\n\"2nd<\/p>\n

Question 3.
\nUsing cofactors of elements of second row, Evaluate
\n\\(\\Delta\\left|\\begin{array}{lll}{1} & {0} & {0} \\\\{0} & {1} & {0} \\\\{0} & {0} & {1}\\end{array}\\right|\\)
\nAnswer:
\n<\/span>C21<\/sub> = 0\u00a0 \u00a0C22<\/sub> = 1\u00a0 \u00a0 \u00a0 C23 <\/sub>= 0
\n\u2234 \u0394 A = 0 x 0 + 1 x 1 + 0 x 0 = 1<\/p>\n

\"KSEEB<\/p>\n

Question 4.
\nUsing cofactors of elements of 3rd column
\n\\(\\Delta=\\left|\\begin{array}{lll}{\\mathbf{1}} & {\\mathbf{x}} & {\\mathbf{y} \\mathbf{z}} \\\\{\\mathbf{1}} & {\\mathbf{y}} & {\\mathbf{z} \\mathbf{x}} \\\\{\\mathbf{1}} & {\\mathbf{z}} & {\\mathbf{x} \\mathbf{y}}\\end{array}\\right|\\)
\nAnswer:
\n<\/span>M13<\/sub> = (z – y) M23<\/sub> = (z-x) M33<\/sub> = (y-x)
\nC13<\/sub> = (z-y) C23<\/sub> = -(z-n), C33<\/sub> = (y – x)
\n\u0394 = yz (z – y) + zx{-(z – x)} + xy (y – x)
\n= yz2<\/sup> – y2<\/sup>z – z2<\/sup>x + zx2<\/sup> + xy2<\/sup> – x2<\/sup>y
\nx2<\/sup> (z – y) + z (y2<\/sup> – z2<\/sup>) + yz (z – y)
\nx2<\/sup> (z – y) + x (y+ z) (y- z) + yz (z – y)
\n(z – y) {x2<\/sup> – x (y + z) + yz}
\n(z – y) {x2<\/sup> – xy – xz + yz}
\n(z – y) {x (x – y) – z (x – y)}
\n(z – y) (x – y) (x – z) = (z – y) (y – x) (z – x)<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\n\\(\\text { If } \\Delta=\\left|\\begin{array}{lll}{\\mathbf{a}_{11}} & {\\mathbf{a}_{12}} & {\\mathbf{a}_{13}} \\\\{\\mathbf{a}_{21}} & {\\mathbf{a}_{22}} & {\\mathbf{a}_{23}} \\\\{\\mathbf{a}_{31}} & {\\mathbf{a}_{32}} & {\\mathbf{a}_{33}}\\end{array}\\right|\\) is a cofactors of aij<\/sub> then the calue of \u0394 is given by of
\n(A) a11<\/sub> A31<\/sub> + a12<\/sub> A32<\/sub> + a13<\/sub> A33
\n<\/sub>(B) an<\/sub> An<\/sub> + a12<\/sub> A21<\/sub> + a13<\/sub> A31
\n<\/sub>(C) a21<\/sub> Au<\/sub> + a22<\/sub> A12<\/sub> + a23<\/sub> A13
\n<\/sub>(D) an<\/sub> An<\/sub> + a21<\/sub> A21<\/sub> + a31<\/sub> A31
\n<\/sub>Answer:
\nAnswer is (D)
\ni.e., a11<\/sub> A11<\/sub> + a21<\/sub>+ a31<\/sub> A31<\/sub><\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 4 Determinants Ex 4.4 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka 2nd PUC Maths Question Bank Chapter 4 Determinants Ex 4.4 2nd PUC Maths Determinants NCERT Text Book …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[82],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/18762"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=18762"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/18762\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=18762"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=18762"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=18762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}