Find the values of x,y,z if the matrix A=⎣⎡0xx2yy−yz−zz⎦⎤ satisfy the equation A′A=I.

Question

Find the values of x,y,z if the matrix A=⎣⎡​0xx​2yy−y​z−zz​⎦⎤​ satisfy the equation A′A=I.

Filo · Accepted Answer

Given,A=⎣⎡​0xx​ 2yy−y​ z−zz​⎦⎤​A′=⎣⎡​02yz​xy−z​x−yz​⎦⎤​I=⎣⎡​100​010​001​⎦⎤​Now, A′A=IPutting values⎣⎡​ 02yz​xy−z​x−y z​⎦⎤​⎣⎡​0xx​2yy−y​z−zz​⎦⎤​⎣⎡​100​010​001​⎦⎤​⎣⎡​ 0(0)+x(x)+x(x)2y(0)+y(x)−y(x)z(0)−z(x)+z(x)​0(2y)+x(y)+x(−y)2y(2y)+y(y)−y(−y)z(2y)−z(y)+z(−y)​0(z)+x(−z)+x(z)2y(z)+y(−z)−y(z)z(z)−z(−z)+z(z)​⎦⎤​=⎣⎡​100​010​0 0 1​⎦⎤​⎣⎡​ 0+x2+x20+xy−xy0−xz+xz​ 0+xy−xy4y2+y2+y22zy−zy−zy​0−xz+xz2zy−zy−zyz2+z2+z2​⎦⎤​=⎣⎡​10 0​01 0​00 1​⎦⎤​⎣⎡​ 2x20 0​ 06y20​003z2​⎦⎤​=⎣⎡​10 0​01 0​001​⎦⎤​Since matrices are equal,corresponding elements are equal,2x2=1x2=21​x=±21​​x=±2​1​6y2=1y2=61​y=±61​​y=±6​1​3z2=1z2=31​z=±31​​z=±3​1​Thus, x=±2​1​,y=±6​1​,z=±3​1​

Question Text	Find the values of $x, y, z$ if the matrix $A = ⎣ ⎡ 0 x x 2 y y - y z - z z ⎦ ⎤$ satisfy the equation $A^{'} A = I .$
Answer Type	Text solution:1
Upvotes	150

Find the values of $x, y, z$ if the matrix $A = ⎣ ⎡ 0 x x 2 y y - y z - z z ⎦ ⎤$ satisfy the equation $A^{'} A = I .$

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Find the values of x,y,z if the matrix A=⎣⎡​0xx​2yy−y​z−zz​⎦⎤​ satisfy the equation A′A=I.

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Find the values of $x, y, z$ if the matrix $A = ⎣ ⎡ 0 x x 2 y y - y z - z z ⎦ ⎤$ satisfy the equation $A^{'} A = I .$