Question

For which value(s) of \( a \) will the matrix \( A=\left[\begin{array}{cc}2 & a \\ -a & 1\end{array}\right] \) be orthogonally diagonalizable? A. \( a=1 \) B. \( a \neq 1 \) C. None of the othor options. D. \( a \neq 2 \) E. For all values of \( a \). \( \mathrm{F}, a=0 \) G. For no values of \( a \).

          For which value(s) of \( a \) will the matrix \( A=\left[\begin{array}{cc}2 & a \\ -a & 1\end{array}\right] \) be orthogonally diagonalizable?
A. \( a=1 \)
B. \( a \neq 1 \)
C. None of the othor options.
D. \( a \neq 2 \)
E. For all values of \( a \).
\( \mathrm{F}, a=0 \)
G. For no values of \( a \).

For which value(s) of a will the matrix A=[
2 a
-a 1
] be orthogonally diagonalizable?
A. a=1
B. a ≠ 1
C. None of the othor options.
D. a ≠ 2
E. For all values of a.
F, a=0
G. For no values of a.

Added by Kristina R.

Higher Engineering Mathematics

John Bird 8th Edition

Chapter 25

Instant Answer

Solved by Expert Linda Hand

Step 1

A matrix is orthogonally diagonalizable if and only if it is symmetric. Show more…

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For which value(s) of \( a \) will the matrix \( A=\left[\begin{array}{cc}2 & a \\ -a & 1\end{array}\right] \) be orthogonally diagonalizable? A. \( a=1 \) B. \( a \neq 1 \) C. None of the othor options. D. \( a \neq 2 \) E. For all values of \( a \). \( \mathrm{F}, a=0 \) G. For no values of \( a \).