Question
If $A =\left[\begin{array}{ll}\alpha & 2 \\ 2 & \alpha\end{array}\right]$ and $\left| A ^3\right|=125$, then $\alpha=$ __________ .
✓
Answer
$\pm 3$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Fill in the blank.
A matrix which is not a square matrix is called a _________ matrix.
A matrix which is not a square matrix is called a _________ matrix.
Fill in the blanks:
The least value of the function $\text{f(x)}=\text{ax}+\frac{\text{b}}{\text{a}}(\text{a}>0,\text{b}>0,\text{x}>0)$ is ______.
→The least value of the function $\text{f(x)}=\text{ax}+\frac{\text{b}}{\text{a}}(\text{a}>0,\text{b}>0,\text{x}>0)$ is ______.
The order of $y^{\prime \prime \prime}+y^2+e^{y^{\prime}}=0$ will be ___________ .
→Fill in the blanks.
The vector equation of the line through the points (3, 4, -7) and (1, -1, 6) is __________.
The vector equation of the line through the points (3, 4, -7) and (1, -1, 6) is __________.
Consider the following equations of curves $x^2= y$ and $y = x.$
On the basis of above information, answer the following questions.
→On the basis of above information, answer the following questions.
- The point(s) of intersection of both the curves is (are).
- (0, 0)(2, 2)
- (0, 0)(1, 1)
- (0, 0)(-1, -1)
- (0, 0)(-2, -2)
- Area bounded by the curves is represented by which of the following graph?
- The value of the integral $\int\limits_{1}^{0}\text{x}\ \text{dx}$ is.
- $\frac{1}{4}$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $1$
- The value of the integral $\int\limits_{0}^{1}\text{x}^2\ \text{dx}$ is.
- $\frac{1}{4}$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $1$
- The value of area bounded by the curves $x^2= y$ and $x = y$ is.
- $\frac{1}{6}\text{ sq}.\text{unit}$
- $\frac{1}{3}\text{ sq}.\text{unit}$
- $\frac{1}{2}\text{ sq}.\text{unit}$
- ${1}\text{ sq}.\text{unit}$
Fill in the blanks.
If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
→If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
If any element of A is not related to any element of A. This relation R is defined on A is know as _________
Fill in the blanks.
The solution of the differential equation $\text{ydx}+(\text{x}+\text{xy})\text{dy}=0$ is ________.
→The solution of the differential equation $\text{ydx}+(\text{x}+\text{xy})\text{dy}=0$ is ________.
Fill in the blanks.
If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to ________.
→If $|\vec{\text{a}}\times\vec{\text{b}}|^2+|\vec{\text{a}}\cdot\vec{\text{b}}|^2=144$ and $|\vec{\text{a}}|=4,$ then $|\vec{\text{b}}|^2$ is equal to ________.
Fill in the blanks:
The values of a for which the function f(x) = sinx - ax + b increases on R are ______.
The values of a for which the function f(x) = sinx - ax + b increases on R are ______.