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Q.18 please step wise answer so that i undestand easily..........

Mehul Verma , 5 Years ago
Grade 12
anser 1 Answers
Vinod Ramakrishnan Eswaran

Last Activity: 5 Years ago

Let the first matrix be A and secound matrix be B So they are asking the product of matrix A and B
 A=\begin{vmatrix} 1 &-1 &2 \\ 0& 2 &-3 \\ 3&-2 & 4 \end{vmatrix}
 
B=\begin{vmatrix} -2 &0 &1 \\ 9& 2 &-3 \\ 6&1 & -2 \end{vmatrix}
 
 
Hence their product would be
 
A*B=\begin{vmatrix} 1 &-1 &2 \\ 0& 2 &-3 \\ 3&-2 & 4 \end{vmatrix}\begin{vmatrix} -2 &0 &1 \\ 9& 2 &-3 \\ 6&1 & -2 \end{vmatrix}
A*B=\begin{vmatrix} 1*-2+-1*9+2*6 &1*0-1*2+2*1 &1*1+3*1+2*-2 \\ 0*-2+2*9+6*-3& 0*0+2*2+1*-3 &0*1-3*2+3*2 \\ 3*-2-9*2+6*4&3*0+2*-2+4*1 & 3*1+2*3-4*2 \end{vmatrix}
 
A*B=\begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 &0 \\ 0 & 0 & 1 \end{vmatrix}=I
Since A*B=I,Multiplying with A-1 on both sides we get
B=A-1                          -(1)
Now from the equations we have 
\begin{vmatrix} 1 & -1 & 2 \\ 0 & 2 &-3 \\ 3 & -2 & 4 \end{vmatrix}\begin{vmatrix} x\\ y\\ z \end{vmatrix}=\begin{vmatrix} 1\\ 1\\ 2 \end{vmatrix}
         A                   X           C
 
A*X=C
Applying A-1 on both sides we get
X=A-1C
But from (1)
B=A-1
hence X=BC
X=\begin{vmatrix} -2 & 0 & 1 \\ 9 & 2 &-3 \\ 6 & 1 & -2 \end{vmatrix}\begin{vmatrix} 1\\ 1\\ 2 \end{vmatrix}
 
\begin{vmatrix} x\\ y\\ z \end{vmatrix}=\begin{vmatrix} (-2*1+0*1+1*2)\\ (9*1+2*1-3*2)\\ (6*1+1*1-2*2) \end{vmatrix}
\begin{vmatrix} x\\ y\\ z \end{vmatrix}=\begin{vmatrix} (0)\\ (5)\\ (3) \end{vmatrix}
Hence x=0,y=5,z=3
 

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