Periodic Matrix

Q. If $\left(\begin{array}{cc}2& 4\\ -1& k\end{array}\right)$ is a nilpotent matrix of index $2,$ then $k$ equals to

1. $2$
2. $-3$
3. $4$
4. $-2$

Q.

A square matrix satisfying $A^{k+1}=A$ is called as periodic matrix.

If k = 2 satisfies the above condition, A becomes an idempotent matrix

1. True

2. False

Q.

Solve: $12÷2(6-7+4)2$

Q.

A square matrix satisfying $A^{k+1}=A$ is called as periodic matrix.

If k = 2 satisfies the above condition, A becomes an idempotent matrix

1. True

2. False

Q.

A square matrix A such that $A^k=A$ for a positive integer k is called a periodic matrix.

1. True

2. False

Q.

A= $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$which of the following is true?

1. A is a periodic matrix with period 1

2. A is an idempotent matrix

3. A is a periodic matrix with period 2

4. A is not an idempotent matrix

Q. Let A, B be square matrix such that A B = 0 and B is non singular then

1. $\left|A\right|$ must be zero but A may non zero
2. A must be zero matrix
3. none of these
4. nothing can be said in general about A

Q.

A is a square matrix such that $A^2=A$, then dot (A) is equal to

Q. If $f\left(x\right)=\left[x\right]+[x+\frac{1}{2}]$, where [.] denotes the greatest integer function, then

1. ${lim}_{x\to \frac{1}{2}+0}f\left(x\right)=1$
2. $f\left(x\right)$ is continuous at $x=\frac{1}{2}$
3. ${lim}_{x\to \frac{1}{2}-}f\left(x\right)=1$
4. $f\left(x\right)$ is discontinuous at $x=\frac{1}{2}$

Q. $A$ and $B$ are two non-singular square matrices each of $3\times 3$ such that $AB=A$ and $BA=B$ and $|A+B|\ne 0$, then $|A+B|$ is -

Q.

In Question 2 what the indexof the matrix A is__

Q.

A= $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$which of the following is true?

1. A is a periodic matrix with period 1

2. A is an idempotent matrix

3. A is a periodic matrix with period 2

4. A is not an idempotent matrix

Q.

A= $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$which of the following is true?

1. A is a periodic matrix with period 1

2. A is an idempotent matrix

3. A is a periodic matrix with period 2

4. A is not an idempotent matrix

Q.

A= $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$which of the following is true?

1. A is a periodic matrix with period 1

2. A is an idempotent matrix

3. A is a periodic matrix with period 2

4. A is not an idempotent matrix

Q. If the matrix $\left[\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 8\\ 3& 5& 10\end{array}\right]$ is singular, then $\lambda =$

1. $-2$
2. $4$
3. $2$
4. $-4$

Q.

A square matrix A such that $A^k=A$ for a positive integer k is called a periodic matrix.

1. True

2. False

Q.

A square matrix A such that $A^k=A$ for a positive integer k is called a periodic matrix.

1. True

2. False

Q.

A square matrix satisfying $A^{k+1}=A$ is called as periodic matrix.

If k = 2 satisfies the above condition, A becomes an idempotent matrix

1. False

2. True

Q.

A square matrix A such that $A^k=A$ for a positive integer k is called a periodic matrix.

1. True

2. False