Solution Of System Of Equations Using Matrix Method: A Step-By-Step Approach

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Solution of System of Equations Using Matrix Method: A Step-by-Step ApproachQuestionSolve the following system of equations using matrix method:𝟐𝒙+𝟑𝒚+𝟏𝟎𝒛=𝟒,𝟒𝒙−𝟔𝒚+𝟓𝒛=𝟏,𝟔𝒙+𝟗𝒚−𝟐𝟎𝒛=𝟐Topic:MatrixSub Topic:Solution of system of equations by matrix methodCLASS-XIISolution:Step-1–Let us assume that:1𝑥=𝑎,1𝑦=𝑏and1𝑧=𝑐, the system takes the form:2𝑎+3𝑏+10𝑐=4………………… (1)4𝑎−6𝑏+5𝑐=1…………………… (2)6𝑎+9𝑏−20𝑐=2…………………. (3)Step-2-Matrix equation and notationsThe above system is given by the matrix equation:AX = B OR X =𝑨−𝟏𝑩WhereA =[23104−6569−20]3𝑋3,B =[412]3𝑋1,X =[𝑎𝑏𝑐]3𝑋1Step-3-Determinant of A|𝐴|=|23104−6569−20|=1200≠0⇒System has a unique solution and hence consistent.Step-4-Cofactors𝐴11=75,𝐴12=110,𝐴13=72𝐴21=150,𝐴22=−100,𝐴23=0𝐴31=75,𝐴32=30,𝐴33=−24Step-5-Adjoint of A

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