Find Aadj A for the matrix A -1-2302-1-452 -

A=1 2302 1 452Now,C11=2 152=9, #160;C12= 0 1 42=4 #160;and #160;C13=02 45=8C21=–2352=19, #160;C22=13 42=14 #160;and #160;C23= 1 2 45=3C31= 232 1= 4, ...

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Standard XII

Mathematics

Inverse of a Matrix

Find Aadj A f...

Question

Find A (adj A) for the matrix $A = [\begin{matrix} 1 & - 2 & 3 \\ 0 & 2 & - 1 \\ - 4 & 5 & 2 \end{matrix}] .$

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Solution

$A = [\begin{matrix} 1 & - 2 & 3 \\ 0 & 2 & - 1 \\ - 4 & 5 & 2 \end{matrix}] Now, C_{11} = |\begin{matrix} 2 & - 1 \\ 5 & 2 \end{matrix}| = 9, C_{12} = - |\begin{matrix} 0 & - 1 \\ - 4 & 2 \end{matrix}| = 4 and C_{13} = |\begin{matrix} 0 & 2 \\ - 4 & 5 \end{matrix}| = 8 C_{21} = - |\begin{matrix} - 2 & 3 \\ 5 & 2 \end{matrix}| = 19, C_{22} = |\begin{matrix} 1 & 3 \\ - 4 & 2 \end{matrix}| = 14 and C_{23} = - |\begin{matrix} 1 & - 2 \\ - 4 & 5 \end{matrix}| = 3 C_{31} = |\begin{matrix} - 2 & 3 \\ 2 & - 1 \end{matrix}| = - 4, C_{32} = - |\begin{matrix} 1 & 3 \\ 0 & - 1 \end{matrix}| = 1 and C_{33} = |\begin{matrix} 1 & - 2 \\ 0 & 2 \end{matrix}| = 2 a d j A = {[\begin{matrix} 9 & 4 & 8 \\ 19 & 14 & 3 \\ - 4 & 1 & 2 \end{matrix}]}^{T} = [\begin{matrix} 9 & 19 & - 4 \\ 4 & 14 & 1 \\ 8 & 3 & 2 \end{matrix}] ∴ A (a d j A) = [\begin{matrix} 25 & 0 & 0 \\ 0 & 25 & 0 \\ 0 & 0 & 25 \end{matrix}]$

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Find A (adj A) for the matrix A=1-2302-1-452.

A=1-2302-1-452Now,C11=2-152=9, C12=-0-1-42=4 and C13=02-45=8C21=--2352=19, C22=13-42=14 and C23=-1-2-45=3C31=-232-1=-4, C32=-130-1=1 and C33=1-202=2adj A=94819143-412T=919-44141832∴A(adj A)=250002500025

Find A (adj A) for the matrix $A = [\begin{matrix} 1 & - 2 & 3 \\ 0 & 2 & - 1 \\ - 4 & 5 & 2 \end{matrix}] .$