Matrices

If A = $\left|\begin{array}{ccc}8& 27& 125\\ 2& 3& 5\\ 1& 1& 1\end{array}\right|$, then the value of A² is equal to

• 0

• 36

• 64

• 3600

The roots of the equation $\left|\begin{array}{ccc}\mathrm{x} - 1& 1& 1\\ 1& \mathrm{x} - 1& 1\\ 1& 1& \mathrm{x} - 1\end{array}\right|$ = 0 are

• 1, 2

• - 1, 2

• - 1, - 2

• 1, - 2

$\left|\begin{array}{ccc}1& 1& 1\\ \mathrm{p}& \mathrm{q}& \mathrm{r}\\ \mathrm{p}& \mathrm{q}& \mathrm{r} + 1\end{array}\right|$ is equal to

• q - p

• q + p

• q

• p

Let A = $\left[\begin{array}{cc}5& 0\\ 1& 0\end{array}\right]$ and B = $\left[\begin{array}{cc}20& 5\\ - 1& 0\end{array}\right]$. If 4A + 5B - C = 0, then C is

• $\left[\begin{array}{cc}5& 25\\ - 1& 0\end{array}\right]$

• $\left[\begin{array}{cc}20& 5\\ - 1& 0\end{array}\right]$

• $\left[\begin{array}{cc}5& - 1\\ 0& 25\end{array}\right]$

• $\left[\begin{array}{cc}120& 25\\ - 1& 0\end{array}\right]$

If U = $\left(\begin{array}{cc}\frac{1}{\sqrt{2}}& \frac{- 1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}\end{array}\right)$, then U^-1 is

• U^T

• U

• I

• 0

If A = $\left(\begin{array}{ccc}0& - 1& 0\\ 1& 0& 0\\ 0& 0& - 1\end{array}\right)$, then A^-1 is

• A^T

• A²

• A

• I

If $\left(\begin{array}{cc}\mathrm{x} + \mathrm{y}& \mathrm{x} - \mathrm{y}\\ 2\mathrm{x} + \mathrm{z}& \mathrm{x} + \mathrm{z}\end{array}\right) = \left(\begin{array}{cc}0& 0\\ 1& 1\end{array}\right)$, then the values of x, y and z are respectively

• 0, 0, 1

• 1, 1, 0

• - 1, 0, 0

• 0, 0, 0

$\left(\begin{array}{ccc}7& 1& 5\\ 8& 0& 0\end{array}\right)\left(\begin{array}{c}2\\ 3\\ 1\end{array}\right) + 5\left(\begin{array}{c}1\\ 0\end{array}\right)$ is equal to

• $\left(\begin{array}{c}16\\ 27\end{array}\right)$

• $\left(\begin{array}{c}27\\ 16\end{array}\right)$

• $\left(\begin{array}{c}15\\ 16\end{array}\right)$

• $\left(\begin{array}{c}16\\ 15\end{array}\right)$

If $\left(\begin{array}{ccc}1& 2& 4\\ 1& 3& 5\\ 1& 4& \mathrm{a}\end{array}\right)$ is singular, then the value of a is

• a = - 6

• a = 5

• a = - 5

• a = 6

If $\left(\begin{array}{ccc}1& 2& - 3\\ 0& 4& 5\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\\ \mathrm{z}\end{array}\right) = \left(\begin{array}{c}1\\ 1\\ 1\end{array}\right)$, then (x, y, z) is equal to

• (1, 6, 6)

• (1, - 6, 1)

• (1, 1, 6)

• (6, - 1, 1)