If a, b, c and d are real numbers such that a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given, $a^2+b^2+c^2+d^2=1$ and $A=\left[\begin{array}{cc}a+ib & c+id \ -c+id & a-ib\end{array}ight]$.First, we calculate the determinant $|A|$:

Vedclass · Accepted Answer

$\left[\begin{array}{cc}a-ib & -c-id \ c-id & a+ib\end{array}ight]$

Vedclass · Answer

(C) Given, $a^2+b^2+c^2+d^2=1$ and $A=\left[\begin{array}{cc}a+ib & c+id \ -c+id & a-ib\end{array}ight]$.First, we calculate the determinant $|A|$:$|A| = (a+ib)(a-ib) - (c+id)(-c+id)$$|A| = (a^2 - (ib)^2) - ((id)^2 - c^2)$$|A| = (a^2 + b^2) - (-d^2 - c^2) = a^2+b^2+c^2+d^2 = 1$.Since $|A|=1$, the inverse $A^{-1}$ is given by the adjugate matrix $	ext{adj}(A)$:$A^{-1} = \frac{1}{|A|} 	ext{adj}(A) = \frac{1}{1} \left[\begin{array}{cc}a-ib & -(c+id) \ -(-c+id) & a+ib\end{array}ight]$$A^{-1} = \left[\begin{array}{cc}a-ib & -c-id \ c-id & a+ib\end{array}ight]$.

If $a, b, c$ and $d$ are real numbers such that $a^2+b^2+c^2+d^2=1$ and $A=\left[\begin{array}{cc}a+ib & c+id \\ -c+id & a-ib\end{array}\right]$, then $A^{-1}$ is equal to

Similar Questions

Find the inverse,by elementary row operations (if possible),of the following matrix: $\left[\begin{array}{cc}1 & -3 \\ -2 & 6\end{array}\right]$

Let $A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$. Then find the value of $(A^{-1}B)^{-1} + (AB^{-1})^{-1}$.

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 1/2 & -1/2 & 1/2 \\ -4 & 3 & c \\ 5/2 & -3/2 & 1/2 \end{bmatrix}$,then:

If the inverse of $\begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix}$ does not exist,then $x=$

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 1 & 4 & 9 \\ 1 & 8 & 27 \end{bmatrix}$,then the value of $|adj\, A|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module