+91-8076753736[email protected]
logo
logo
-->

Determinants

Question
CBSEENMA12034842
Wired Faculty App

Use matrix method to solve the following system of equations:
3x – 4y + 2z = – 1
2x + 3y + 5z = 7
x + z = 2 

Solution

The given equations are
3x – 4y + 2z = – 1
2x + 3y + 5z = 7
x + 0y + z = 2
These equations can be written as
                open square brackets table row 3 cell space space minus 4 end cell cell space space space 2 end cell row 2 cell space space space space space 3 end cell cell space space 5 end cell row 1 cell space space space space 0 end cell cell space space 1 end cell end table close square brackets space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space open square brackets table row cell negative 1 end cell row cell space 7 end cell row cell space 2 end cell end table close square brackets
or      AX space equals space straight B space space where space straight A space equals space open square brackets table row 3 cell space space space minus 4 end cell cell space space space 2 end cell row 2 cell space space space space space 3 end cell cell space space 5 end cell row 1 cell space space space space 0 end cell cell space space space 1 end cell end table close square brackets comma space space space space space straight X space equals space open square brackets table row straight x row straight y row straight z end table close square brackets comma space space straight B space equals space open square brackets table row cell negative 1 end cell row cell space 7 end cell row cell space 2 end cell end table close square brackets
          open vertical bar straight A close vertical bar space equals space open vertical bar table row 3 cell space space space minus 4 end cell cell space space space 2 end cell row 2 cell space space space space 3 end cell cell space space 5 end cell row 1 cell space space 0 end cell cell space space 1 end cell end table close vertical bar space equals space 3 open vertical bar table row 3 cell space space space 5 end cell row 0 cell space space 1 end cell end table close vertical bar minus left parenthesis negative 4 right parenthesis space open vertical bar table row 2 cell space space space 5 end cell row 1 cell space space 1 end cell end table close vertical bar plus 2 open vertical bar table row 2 cell space space space 3 end cell row 1 cell space space 0 end cell end table close vertical bar space space space space space space space equals 3 space left parenthesis 3 minus 0 right parenthesis plus 4 space left parenthesis 2 minus 5 right parenthesis space plus space 2 space left parenthesis 0 minus 3 right parenthesis space equals space 9 minus 12 minus 6 space equals space minus 9
Co-factors of the elements of first row of | A | are
open vertical bar table row 3 cell space space 5 end cell row 0 cell space space 1 end cell end table close vertical bar comma space space space minus open vertical bar table row 2 cell space space 5 end cell row 1 cell space space 1 end cell end table close vertical bar comma space open vertical bar table row 2 cell space space 3 end cell row 1 cell space space 0 end cell end table close vertical bar

i.e., 3, 3, – 3 respectively
Co-factors of the elements of second row of | A | are
negative open vertical bar table row cell negative 4 end cell cell space space space space 2 end cell row 0 cell space space space 1 end cell end table close vertical bar comma space space space space open vertical bar table row 3 cell space space space space 2 end cell row 1 cell space space space 1 end cell end table close vertical bar comma space space minus open vertical bar table row 3 cell space space space space minus 4 end cell row 1 cell space space space space space space space 0 end cell end table close vertical bar

i.e., 4, 1, – 4 respectively
Co-factors of the elements of third row of | A | are
                    open vertical bar table row cell negative 4 end cell cell space space space 2 end cell row 3 cell space space 5 end cell end table close vertical bar comma space space minus open vertical bar table row 3 cell space space space space space 2 end cell row 2 cell space space space space 5 end cell end table close vertical bar comma space space space open vertical bar table row 3 cell space space space space minus 4 end cell row 2 cell space space space space space space 3 end cell end table close vertical bar
i.e., – 26, – 11, 17 respectively
                     adj space straight A space equals space open square brackets table row 3 cell space space space space space 3 end cell cell space space space minus 3 end cell row 4 cell space space space space 1 end cell cell space minus 4 end cell row cell negative 26 end cell cell space minus 11 end cell cell space space 17 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell space 3 end cell cell space space space space 4 end cell cell space space space minus 26 end cell row cell space space 3 end cell cell space space space space 1 end cell cell space minus 11 end cell row cell negative 3 end cell cell space space minus 4 end cell cell space space space 17 end cell end table close square brackets space space space space straight A to the power of negative 1 end exponent space equals space space fraction numerator adj. space straight A over denominator open vertical bar straight A close vertical bar end fraction space equals space minus 1 over 9 open square brackets table row 3 cell space space space space space 4 end cell cell space space space space minus 26 end cell row 3 cell space space space space 1 end cell cell space minus 11 end cell row cell negative 3 end cell cell space space minus 4 end cell cell space space space 17 end cell end table close square brackets Now space space space AX space equals space straight B space space space space space space space rightwards double arrow space space space space straight X space equals space straight A to the power of negative 1 end exponent straight B space rightwards double arrow space space space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space minus 1 over 9 open square brackets table row 3 cell space space space space 4 end cell cell negative 26 end cell row 3 cell space space space space 1 end cell cell negative 11 end cell row cell negative 3 end cell cell negative 4 end cell cell space space space 17 end cell end table close square brackets space open square brackets table row cell negative 1 end cell row cell space 7 end cell row cell space 2 end cell end table close square brackets rightwards double arrow space space space space space space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space minus 1 over 9 open square brackets table row cell negative 3 plus 28 minus 52 end cell row cell negative 3 plus 7 minus 22 end cell row cell 3 minus 28 plus 34 end cell end table close square brackets space space space rightwards double arrow space space space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space minus 1 over 9 open square brackets table row cell negative 27 end cell row cell negative 18 end cell row cell space space space 9 space end cell end table close square brackets rightwards double arrow space space space space space space space open square brackets table row straight x row straight y row straight z end table close square brackets space equals space open square brackets table row cell space space space 3 end cell row cell space space space 2 end cell row cell negative 1 end cell end table close square brackets space space space space space space space rightwards double arrow space space space space straight x space equals space 3 comma space space space straight y space equals space 2 comma space space space straight z space equals space minus 1

Some More Questions From Determinants Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation