Há conceitos que definem uma matriz ser uma matriz ortogonal. Desse modo, considere a matriz ortogonal A equals open square brackets table row cell...
Há conceitos que definem uma matriz ser uma matriz ortogonal. Desse modo, considere a matriz ortogonal A equals open square brackets table row cell 1 third end cell cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell row cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell cell fraction numerator negative 1 over denominator 3 end fraction end cell end table close square brackets.
Assinale a alternativa correta que contém a matriz inversa A to the power of negative 1 end exponent.
Alternativas:
a)
A to the power of negative 1 end exponent equals open square brackets table row cell fraction numerator negative 1 over denominator 3 end fraction end cell cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell row cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell cell 1 third end cell end table close square brackets
Alternativa assinalada
b)
A to the power of negative 1 end exponent equals open square brackets table row cell 1 third end cell cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell row cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell cell fraction numerator negative 1 over denominator 3 end fraction end cell end table close square brackets
c)
A to the power of negative 1 end exponent equals open square brackets table row cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell cell 1 third end cell row cell fraction numerator negative 1 over denominator 3 end fraction end cell cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell end table close square brackets
d)
A to the power of negative 1 end exponent equals open square brackets table row cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell cell fraction numerator negative 1 over denominator 3 end fraction end cell row cell 1 third end cell cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell end table close square brackets
e)
A to the power of negative 1 end exponent equals open square brackets table row 1 0 row 0 1 end table close square brackets
💡 1 Resposta
Ed 
A alternativa correta é a letra a) A to the power of negative 1 end exponent equals open square brackets table row cell fraction numerator negative 1 over denominator 3 end fraction end cell cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell row cell fraction numerator 2 square root of 2 over denominator 3 end fraction end cell cell 1 third end cell end table close square brackets.
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