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adOrmaPem6r
2021-11-23
Answered

Given the following vector X, find anon zero square marix A such that AX=0;

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$$X=\left[\begin{array}{c}8\\ 6\\ -7\end{array}\right]$$

$$A=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$$

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Squairron

Answered 2021-11-24
Author has **7** answers

Definition used -

Product of two matrices -

The product of two matrices is possible if the number of columns of the first matrix is equal to the number of rows of the second matrix.

Row element of the first matrix and the corresponding column element of the second matrix multiplied and add.

Given:

$$X=\left[\begin{array}{c}8\\ 6\\ -7\end{array}\right]$$

Let$$A=\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$$

Here a, b, c, d, e, f, g, and h are non-zero.

AX=0

$$\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$$

$8a+6b-7c=0$

$8d+6e-7f=0$

$8g+6h-7i=0$

So we have to choose any three numbers which staifies these equations.

$a=1,b=1$ and $c=2$ will stsify this equation

So we can write matrix-

$$A=\left[\begin{array}{ccc}1& 1& 2\\ -1& -1& -2\\ 2& 2& 4\end{array}\right]$$

Product of two matrices -

The product of two matrices is possible if the number of columns of the first matrix is equal to the number of rows of the second matrix.

Row element of the first matrix and the corresponding column element of the second matrix multiplied and add.

Given:

Let

Here a, b, c, d, e, f, g, and h are non-zero.

AX=0

So we have to choose any three numbers which staifies these equations.

So we can write matrix-

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