Question

Find formulas for​ X, Y, and Z in terms of​ A, B, and C. It may be necessary to make assumptions about the size or invertability of a matrix in order to produce a formula.​ [Hint: Compute the product on the​ left, and set it equal to the right​ side.]

Answer 1

Answer:

The solution is given in the attachments.

Answer 2

The required values are,

$x=\frac{1}{A} \\z=\frac{1}{C} \\y=-\frac{B}{AC}$

Equivalent matrix:

Matrix equivalence is an equivalence relation on the space of

For two rectangular matrices of the same size, their equivalence can also be characterized by the following conditions The matrices can be transformed into one another by a combination of elementary row and column operations.

Let the matrix be,

$\left[\begin{array}{ccc}x&0\\y&z\end{array}\right] \left[\begin{array}{ccc}A&0\\B&C\end{array}\right] =\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\\left[\begin{array}{ccc}x\times A+0\times B&0\times +0\times C\\y\times A+B\times Z&y\times 0+z\times c\end{array}\right] =\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] \\\\x\times A=1\\x=\frac{1}{A} \\z\times c=1\\z=\frac{1}{C} \\y\times A+B\times z=0\\\\y=-\frac{B}{AC}$

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