// Numbas version: exam_results_page_options {"name": "Custom Marking version of Ex 6 Cofactors, Determinant and Inverse of a 3x3 matrix (CC)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "

If \$A=\\left( \\begin{array}{ccc} a & b & c \\\\d & e&f\\\\ g&h&j \\end{array} \\right),\$

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Cofactors are given by \$A=\\left( \\begin{array}{ccc} a & b & c \\\\d & e&f\\\\ g&h&j \\end{array} \\right),\$

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Cof11 =\$+\\left| \\begin{array}{ccc} e&f\\\\ h&j \\end{array} \\right|,\$

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Cof12 =\$-\\left| \\begin{array}{ccc} d & f\\\\ g&j \\end{array} \\right|,\$

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Cof13 =\$+\\left| \\begin{array}{ccc} d & e\\ g&h\\end{array} \\right|,\$

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Cof21 =\$-\\left| \\begin{array}{ccc} b & c \\\\h&j \\end{array} \\right|,\$

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Cof22 =\$+\\left| \\begin{array}{ccc} a & c \\\\ g&j \\end{array} \\right|,\$

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Cof23 =\$-\\left| \\begin{array}{ccc} a & b \\\\g&h\\end{array} \\right|,\$

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Cof31 =\$+=\\left| \\begin{array}{ccc} b & c \\\\e&f\\end{array} \\right|,\$

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Cof32 =\$-\\left| \\begin{array}{ccc} a & c \\\\d & f\\end{array} \\right|,\$

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Cof33 =\$+\\left| \\begin{array}{ccc} a & b\\\\d & e \\end{array} \\right|,\$

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Then, the determinant of A is given by the sum of the product of any row ( or column) elements by their cofactors

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e.g row 1 determinant = a*cof11+b*cof12+c*cof13

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and the inverse of A is given by the ratio of the adjoint(A) and the deteminant of A

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cof11 & cof21 & cof31 \\\\cof12 & cof22&cof32\\\\ cof13&cof23&cof33 \\end{array} \\right),\\]

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inverse of A=\$\\frac{1}{det(A)}*\\left( \\begin{array}{ccc} cof11 & cof21 & cof31 \\\\cof12 & cof22&cof32\\\\ cof13&cof23&cof33 \\end{array} \\right),\$

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Calculate the nine cofactors of A=$\\var{matrixA}$?

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$A _{11}$ cofactor in position 1,1[[0]]

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$A_{12}$ cofactor in position 1,2[[1]]

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$A_{13}$ cofactor in position 1,3[[2]]

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$A_{21}$ cofactor in position 2,1[[3]]

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$A_{22}$ cofactor in position 2,2[[4]]

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$A_{23}$ cofactor in position 2,3[[5]]

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$A_{31}$ cofactor in position 3,1[[6]]

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$A_{32}$ cofactor in position 3,2[[7]]

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$A_{33}$ cofactor in position 3,3[[8]]

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What is the determinant of A=$\\var{matrixA}$?

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[[0]]

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What is the inverse of A=$\\var{matrixA}$? Cofactors will be accepted as fractions or correct to 2 decimal places.

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[[0]]

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cof23

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pupil

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Cofactors Determinant and inverse of a 3x3 matrix.

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