Explanation Given: Matrices, A = [ 1 2 1 5 ] and B = [ − 3 5 ] . Formula used: X = A − 1 B Calculation: As per the equation provided in the question, A X = B So, the solution is, X = A − 1 B Now, calculate A − 1 . As per the definition of inverse A A − 1 = I where I is an identity matrix of order same as that of the matrix A . Therefore, [ 1 2 1 5 ] A − 1 = [ 1 0 0 1 ] Now transform the matrix A into 2 × 2 identity matrix. So, [ 1 2 1 5 ] A − 1 = [ 1 0 0 1 ] Now, use the operation R 2 → R 2 − R 1 . So, [ 1 2 1 − 1 5 − 2 ] A − 1 = [ 1 0 0 − 1 1 − 0 ] [ 1 2 0 3 ] A − 1 = [ 1 0 − 1 1 ] Use the operation R 1 → 3 R 1 − 2 R 2 . So, [ 3 ( 1 ) − 2 ( 0 ) 3 ( 2 ) − 2 ( 3 ) 0 3 ] A − 1 = [ 3 ( 1 ) − 2 ( − 1 ) 3 ( 0 ) − 2 ( 1 ) − 1 1 ] [ 3 − 0 6 − 6 0 3 ] A − 1 = [ 3 + 2 0 − 2 − 1 1 ] [ 3 0 0 3 ] A − 1 = [ 5 − 2 − 1 1 ] Now, take the common value 3 from A and then divide both sides by 3

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ISBN: 9780134773285

Author: MULLINS

Publisher: YUZU

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Chapter 6.6, Problem 2E

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EBK MATHEMATICS WITH APPLICATIONS IN TH

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