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CBSE Class 12-science Answered

how to solve the adjoint of 3×3 matrix
question image
Asked by rahulsharmaaps4 | 03 Jan, 2023, 10:46: AM
answered-by-expert Expert Answer
Let us do elementary operations on given matrix and unit matrix as shown below
 
 
begin mathsize 14px style open square brackets table row 1 0 0 row 0 1 0 row 59 69 cell negative 1 end cell end table close square brackets space equals space open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets cross times A end style
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R3 - 59 R1
 
begin mathsize 14px style open square brackets table row 1 0 0 row 0 1 0 row 0 69 cell negative 1 end cell end table close square brackets space equals space open square brackets table row 1 0 0 row 0 1 0 row cell negative 59 end cell 0 1 end table close square brackets cross times A end style
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R3 - 69R2
 
begin mathsize 14px style open square brackets table row 1 0 0 row 0 1 0 row 0 0 cell negative 1 end cell end table close square brackets space equals space open square brackets table row 1 0 0 row 0 1 0 row cell negative 59 end cell cell negative 69 end cell 1 end table close square brackets cross times A end style
-------------------------------
 
R3 × (-1)
 
begin mathsize 14px style open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets space equals space open square brackets table row 1 0 0 row 0 1 0 row 59 69 cell negative 1 end cell end table close square brackets cross times A end style
 
Inverse of given matrix is
begin mathsize 14px style space open square brackets table row 1 0 0 row 0 1 0 row 59 69 cell negative 1 end cell end table close square brackets end style

 
 
Answered by Thiyagarajan K | 03 Jan, 2023, 03:14: PM
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