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Find formulas for X, Y, and Z in terms of A, B, and C, and justify your calculations. In some cases, you may need to make assumptions about the size of a matrix in order to produce a formula. [Hint: Compute the product on the left, and set it equal to the right side.]$\left[\begin{array}{ccc}{X} & {0} & {0} \\ {Y} & {0} & {I}\end{array}\right]\left[\begin{array}{cc}{A} & {Z} \\ {0} & {0} \\ {B} & {I}\end{array}\right]=\left[\begin{array}{cc}{I} & {0} \\ {0} & {I}\end{array}\right]$

$\begin{array} { | l | l | } \hline X = A ^ { - 1 } \\ { Y } & { = - B A ^ { - 1 } } \\ { Z } & { = 0 } \end{array}$

Algebra

Chapter 2

Matrix Algebra

Section 4

Partitioned Matrices

Introduction to Matrices

Campbell University

Oregon State University

McMaster University

Lectures

01:32

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Okay, So in this purpose left inside in this equation, you used to like 00 y zero. I not tried by a Z 00 b i and off this summit seven matrixes are petitioned conform obl e So we can just directly use the matrix multiplication. So we have X a x z. So the result will be a two by two matrix and by so this is 11 site in the right hand side of this equation because toe and identity matrix, that means X a closed toe I, which gives us X equals toe a evers and that we know that's why, um why a class B equals 20 that gives us why he caused to minus Pete times a humors and the four Z We know that xz cause zero. That means he has to be zero. So this is the solutions. Are these other solutions to this program

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