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

Struggling with matrices? This Homework Solution breaks it down for you with step-by-step clarity.

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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:πŸπ’™+πŸ‘π’š+πŸπŸŽπ’›=πŸ’,πŸ’π’™βˆ’πŸ”π’š+πŸ“π’›=𝟏,πŸ”π’™+πŸ—π’šβˆ’πŸπŸŽπ’›=𝟐Topic:MatrixSub Topic:Solution of system of equations by matrix methodCLASS-XIISolution:Step-1–Let us assume that:1π‘₯=π‘Ž,1𝑦=𝑏and1𝑧=𝑐, the system takes the form:2π‘Ž+3𝑏+10𝑐=4………………… (1)4π‘Žβˆ’6𝑏+5𝑐=1…………………… (2)6π‘Ž+9π‘βˆ’20𝑐=2…………………. (3)Step-2-Matrix equation and notationsThe above system is given by the matrix equation:AX = B OR X =π‘¨βˆ’πŸπ‘©WhereA =[23104βˆ’6569βˆ’20]3𝑋3,B =[412]3𝑋1,X =[π‘Žπ‘π‘]3𝑋1Step-3-Determinant of A|𝐴|=|23104βˆ’6569βˆ’20|=1200β‰ 0β‡’System has a unique solution and hence consistent.Step-4-Cofactors𝐴11=75,𝐴12=110,𝐴13=72𝐴21=150,𝐴22=βˆ’100,𝐴23=0𝐴31=75,𝐴32=30,𝐴33=βˆ’24Step-5-Adjoint of A

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