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Maths-

General

Easy

Question

If $open square brackets table row alpha beta row gamma cell negative alpha end cell end table close square brackets$ is to be square root of two rowed unit matrix, then $alpha comma beta text and end text gamma$ should satisfy the relation-

$1 + α^{2} + β y = 0$
$1 - α^{2} - β γ = 0$
$1 - α^{2} + β γ = 0$
$α^{2} + β γ = 1$

The correct answer is: $1 minus alpha squared minus beta gamma equals 0$

$open square brackets table row alpha beta row gamma cell negative alpha end cell end table close square brackets$ = $square root of open square brackets table row 1 0 row 0 1 end table close square brackets end root$
$rightwards double arrow open square brackets table row alpha beta row gamma cell negative alpha end cell end table close square brackets squared$ = $open square brackets table row 1 0 row 0 1 end table close square brackets$
$rightwards double arrow open square brackets table row cell alpha squared plus beta gamma end cell 0 row 0 cell beta gamma plus alpha squared end cell end table close square brackets$ = $open square brackets table row 1 0 row 0 1 end table close square brackets$
Hence choice (B) is true.

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If A_r = $open parentheses table row r cell r minus 1 end cell row cell r minus 1 end cell r end table close parentheses$ where r is a natural number then |A₁| + |A₂| + |A₃| +……+ |A₂₀₀₆| must be equal to-

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parallel

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