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

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

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

Let A and B be square matrices of the same order, then which of the following is/are true?

माना A व B समान कोटि वाले वर्ग आव्यूह हैं, तब निम्न में से कौनसा/कौनसे विकल्प सही है/हैं?

1. If A^T = A, then A is a symmetric matrix
   
   यदि A^T = A, तब A एक सममित आव्यूह है
2. If A² = I, then A is an invertible matrix
   
   यदि A² = I, तब A एक व्युत्क्रमणीय आव्यूह है
3. If A + A^T = 0, then A is a symmetric matrix
   
   यदि A + A^T = 0, तब A एक सममित आव्यूह है
4. If AB = O, then either A or B must be a zero matrix
   
   यदि AB = O, तब या तो A या B शून्य आव्यूह होगा

Q.

Which among the following are triangular matrices?

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

2. $\left[\begin{array}{ccc}5& 0& 0\\ 1& 2& 0\\ 0& 3& 3\end{array}\right]$

3. $\left[\begin{array}{ccc}1& 3& 0\\ 2& 1& 3\\ 0& 2& 1\end{array}\right]$

4. $\left[\begin{array}{ccc}2& 3& 9\\ 1& 5& 0\\ 6& 0& 0\end{array}\right]$

Q.

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

1. True

2. False

Q. The value of determinant of lower triangular matrix $\left[\begin{array}{ccc}a& 0& 0\\ d& b& 0\\ e& f& c\end{array}\right]$ is

1. $def$
2. $abc$
3. $0$
4. None of these

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

1. $a_{ij}\ne 0$, for i>j
2. $a_{ij}=0$, for i>j
3. $a_{ij}=0$, for i<j
4. $Noneofthese$

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

1. $a_{ij}\ne 0$, for i>j
2. $a_{ij}=0$, for i>j
3. $a_{ij}=0$, for i<j
4. $Noneofthese$

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