Grade 12Algebra

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

Question image for Q.18 please step wise answer so that i undestand

Mehul Verma

7 Years agoGrade 12

Vinod Ramakrishnan Eswaran

Approved Tutor Answer7 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

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

Mehul Verma

1 Answer

Vinod Ramakrishnan Eswaran

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

Mehul Verma

1 Answer

Vinod Ramakrishnan Eswaran

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