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Matrices And Systems

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Running Head: SYSTEMS AND MATRICES 1 Systems and Matrices Name Institution Instructor Date SYSTEMS AND MATRICES 2 Problem 1 3x − 7y = 15 3x + 7y = 15 Solution Using substitution method x= 15+7y 3 Substituting the value of x in the second equation 15 + 7y 3( ) + 7y = 15 3 15 + 7y + 7y = 15 14y = 15 − 15 14y = 0 y=0 x= 15+7y 3 = 15+7×0 3 =5 𝐚𝐧𝐬𝐰𝐞𝐫𝐬 𝐱 = 𝟓 𝐲=𝟎 Problem 2 Find the cofactor of each element in the second row of each matrix. 𝟏 [𝟏 𝟎 −𝟏 𝟐 𝟎 𝟐] −𝟑 𝟏 Solution Second row Cofactor of 1 −1 2 | | = (−1 × 1) − (2 × −3) = −1 + 6 = 5 −3 1 SYSTEMS AND MATRICES 3 𝐀𝐧𝐬𝐰𝐞𝐫 = −𝟓 Cofactor of 0 1 2 | | = (1 × 1) − (2 × 0) = 1 − 0 = 1 0 1 𝐀𝐧𝐬𝐰𝐞𝐫 = 𝟏 Cofactor of 2 1 −1 | | = (1 × −3) − (−1 × 0) = −3 0 −3 𝐀𝐧𝐬𝐰𝐞𝐫 = 𝟑 Problem 3 Solve each nonlinear system of equations. Give all solutions, including those with non-real complex components. 𝑥2 + 𝑦2 = 0 2x 2 − 3y 2 = 0 Solution 𝑥 2 = −𝑦 2 Substituting x 2 on the second equation −2𝑦 2 − 3𝑦 2 = 0 −5𝑦 2 = 0 𝑦=0 𝑥 2 = −02 = 0 ? ...
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