Can You Solve This Cambridge University Maths Problem?

<p>We can factor out&nbsp;<em>x</em>,&nbsp;<em>y</em>&nbsp;and&nbsp;<em>z</em>&nbsp;in the right hand side. This cancels out the denominator of&nbsp;<em>x</em>,&nbsp;<em>y</em>&nbsp;and&nbsp;<em>z</em>&nbsp;when we substitute in the expressions given in the question:</p> <p><img alt="" src="https://miro.medium.com/v2/resize:fit:297/1*0HF6_4mWcxmb1ZpyU5zLpg.png" style="height:443px; width:297px" /></p> <p>Written by me in LaTeX</p> <p>Which is what we needed to show.&nbsp;</p> <p>Next, we need to show that&nbsp;<em>yz + zx + xy = -1.&nbsp;</em>To obtain an expression in&nbsp;<em>x</em>,&nbsp;<em>y</em>, and&nbsp;<em>z</em>, we should use the&nbsp;<strong>determinant&nbsp;</strong>of the matrix, which we will call&nbsp;<em>A.&nbsp;</em>What is the determinant of&nbsp;<em>A</em>?</p> <p>We are given that&nbsp;<em>A</em>&nbsp;maps the following vector to the zero vector:</p> <p><a href="https://medium.com/new-writers-welcome/can-you-solve-this-cambridge-university-maths-problem-4927aef64092"><strong>Website</strong></a></p>