If the sum of binomial coefficients in the expansion of \( (x + y)^{n} \) is 256, then the greatest binomial coefficient occurs in which one of the following terms?
If
\( \begin{bmatrix} x & 1 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = \begin{bmatrix} 45 \end{bmatrix} \)
then which one of the following is a value of \( x \)?
If
\( A = \begin{bmatrix} y & z & x \\ z & x & y \\ x & y & z \end{bmatrix} \)
where \( x, y, z \) are integers, is an orthogonal matrix, then what is the value of \( x^{2} + y^{2} + z^{2} \)?
Consider the following in respect of a non-singular matrix \( M \):
I. \( |M^{2}| = |M|^{2} \)
II. \( |M| = |M^{-1}| \)
III. \( |M| = |M^{T}| \)
How many of the above are correct?
If
\( A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix} \)
then what is \( A^{2} - 4A \) equal to?
where \( I_{3} \) is the identity matrix of order 3.
If
\( A = \begin{bmatrix} x & y & z \\ y & z & x \\ z & x & y \end{bmatrix} \)
where \( x, y, z \) are integers, is an orthogonal matrix, then what is \( A^{2} \) equal to?
