Step 1:

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The equations are $\"\"$

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Write the equations into matrix form $\"\"$ , where $\"\"$ is coefficient matrix,

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$\"\"$ is variable matrix and $\"\"$ is constant matrix.

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$\"\"$ \ \

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Definition of inverse matrix :

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If $\"\"$ is an $\"\"$ then $\"\"$ , where $\"\"$ .

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Let $\"\"$ , then $\"\"$ .

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$\"\"$

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$\"\"$ , then $\"\"$ has an inverse. \ \

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(a)

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Find the inverse matrix $\"\"$ .

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$\"\"$

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$\"\"$

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(b)

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Find $\"\"$ values of first system. \ \ \ \ $\"\"$ \ \

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Substitute $\"\"$ .

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$\"\"$

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Solution:

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(a) The inverse matrix is $\"\"$

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(b) The value of first system is $\"\"$ .

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(2)

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Step 1:

\

The equations are $\"\"$

\

Write the equations into matrix form $\"\"$ , where $\"\"$ is coefficient matrix,

\

$\"\"$ is variable matrix and $\"\"$ is constant matrix.

\

$\"\"$ \ \

\

Definition of inverse matrix :

\

If $\"\"$ is an $\"\"$ then $\"\"$ , where $\"\"$ .

\

Let $\"\"$ , then $\"\"$ .

\

$\"\"$

\

$\"\"$ , then $\"\"$ has an inverse. \ \

\

(a)

\

Find the inverse matrix $\"\"$ .

\

$\"\"$

\

\

$\"\"$

\

(b)

\

Find $\"\"$ values of first system. \ \ \ \ $\"\"$ \ \

\

Substitute $\"\"$ .

\

$\"\"$

\

Solution:

\

(a) The inverse matrix is $\"\"$

\

(b) The value of first system is $\"\"$ .