If for the matrix, A $=\left[\begin{array}{cc}\hfill 1\hfill & \hfill -\alpha \hfill \\ \hfill \alpha \hfill & \hfill \beta \hfill \end{array}\right],A{A}^T=I_2,$ then the value of 4 + 4 is

<p><math><mrow><mn>1</mn><mo>+</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>⇒</mo><mi>α</mi><mo>=</mo><mn>0</mn></mrow></math></p><p><math><mrow><mo>&amp;</mo><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>⇒</mo><msup><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mo>±</mo><mn>1</mn></mrow></math></p><p><math><mrow><mo>&amp;</mo><mi>α</mi><mo>−</mo><mi>α</mi><mi>β</mi><mo>=</mo><mn>0</mn><mo>⇒</mo><mi>α</mi><mrow><mo> (</mo><mrow><mn>1</mn><mo>−</mo><mi>β</mi></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>⇒</mo><mi>α</mi><mo>=</mo><mn>0</mn><mtext> </mtext><mtext> </mtext><mi>o</mi><mi>r</mi><mtext> </mtext><mtext> </mtext><mi>β</mi><mo>=</mo><mn>1</mn></mrow></math></p><p>= 0 &amp; = 1 or = 0 &amp; = 1</p><p>4 + 4 = 1</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment