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If a, b, c and d are real numbers such that a^2+b^2+c^2+d^2=1

Question

If $a, b, c$ and $d$ are real numbers such that $a^{2} + b^{2} + c^{2} + d^{2} = 1$ and $I f A = [a + ib - c + i d c + i d a - ib]$ then $A^{- 1} =$

[a + ib c - i d - c - i d a - ib]

[a - ib - c + i d c + i d a + ib]

[a - ib c - i d - c - i d a + ib]

[a + ib c - i d c + i d a - ib]

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a, b, c

and

d

are real numbers such that

a^{2} + b^{2} + c^{2} + d^{2} = 1

and

I f A = [a + ib - c + i d c + i d a - ib]

then

A^{- 1} =

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Text solutionVerified

A = [a + ib - c + i d c + i d a - ib]

A^{- 1} = \frac{a d j ( A )}{∣ A ∣}

∣ A ∣ = (a + ib) (a - ib) - (c + i d) (^{-} c + i d)

∣ A ∣ = a^{2} + b^{2} - [- d^{2} - c^{2}] = a^{2} + b^{2} + c^{2} + d^{2}

∣ A ∣ = 1

M_{11} = a - ib

M_{12} = c - i d

M_{21} = - c - i d

M_{22} = a + ib

\Rightarrow

cofactor matrix = \begin{bmatrix}a-ib&-c-id\\c-id&a+ib \end{bmatrix}

Adj(A) = \begin{bmatrix}a-ib&-c-id\\c-id&a+ib\end{bmatrix}

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Question Text	If $a, b, c$ and $d$ are real numbers such that $a^{2} + b^{2} + c^{2} + d^{2} = 1$ and $I f A = [a + ib - c + i d c + i d a - ib]$ then $A^{- 1} =$
Answer Type	Text solution:1
Upvotes	150