Triangular Matrix

Q.

Sum of an upper triangular matrix and lower triangular matrix can result in a triangular matrix.

1. True

2. False

Q.

What are the types of Matrices?

Q.

Which among the following are classifications of triangular matrices?

1. Right triangular matrices

2. Upper triangular matrices

3. Middle triangular matrices

4. lower triangular matrices

Q.

Square matrix $[a_{ij}{]}_{n\times n}$ will be an upper triangular matrix, if

1. $Noneofthese$

2. $a_{ij}\ne 0$, for i>j

3. $a_{ij}=0$, for i>j

4. $a_{ij}=0$, for i<j

Q. A given convex pentagon ABCDE has the property that the area of each of the five triangles ABC, BCD, CDE, DEA, and EAB is unity. Show that all pentagons with the above property have same area, and calculate the area. Show, further that there are infinitely many non-congruent pentagons having the above property.

Q. The matrix $\left[\begin{array}{ccc}2& 5& -7\\ 0& 3& 11\\ 0& 0& 9\end{array}\right]$ is known as

1. Skew symmetric matrix
2. Symmetric matrix
3. Diagonal matrix
4. Upper triangular matrix

Q. If $\left[\begin{array}{cccc}1& 0& 0& 0\\ 2& 3& 0& 0\\ 4& 5& 6& 0\\ 7& 8& 9& 10\end{array}\right]$, then A is

1. An upper triangular matrix
2. A null matrix
3. A lower triangular matrix
4. None of these

Q. If in a square matrix $A=\left[a_{ij}\right]$, we find that $a_{ij}=a_{ji}\forall i,j$ then $A$ is a:

1. Symmetric matrix
2. Diagonal matrix
3. Transpose matrix
4. Skew-symmetric matrix

Q.

Which among the following are triangular matrices?

1. 

2. 

3. 

4.