If for the matrix, A = 1 - α α β ,   A A T = I 2 , then the value of α 4 + β 4 is :

Question

If for the matrix, A = 1 - &#945; &#945; &#946; , &#160; A A T = I 2 , then the value of &#945; 4 + &#946; 4 is :

Aicharya · Accepted Answer

A = 1 - &#945; &#945; &#946; &#160;&#160; A A T = I 2 &#8658; 1 - &#945; &#945; &#946; 1 &#945; - &#945; &#946; = 1 0 0 1 &#8658; 1 + &#945; 2 &#945; - &#945; &#946; &#945; - &#945; &#946; &#945; 2 + &#946; 2 = 1 0 0 1 &#8658; 1 + &#945; 2 = 1 &#160; &#38; &#160; &#945; 2 + &#946; 2 = 1 &#8658; &#945; 2 = 0 &#160; &#38; &#160; &#946; 2 = 1 &#8756; &#160; &#945; 4 = 0 &#160; &#38; &#160; &#946; 4 = 1 &#8756; &#160; &#945; 4 + &#946; 4 = 1

If for the matrix, A = 1 - α α β ,   A A T = I 2 , then the value of α 4 + β 4…

Solution

If for the matrix, A = 1 - &#945; &#945; &#946; , &#160; A A T = I 2 , then the value of &#945; 4 + &#946; 4…

Solution

If for the matrix, A = 1 - α α β , A A T = I 2 , then the value of α 4 + β 4…