If A = (1 2 3), then the rank of AA^T is ________.

The rank of m x n matrix whose elements are unity is ________.

if T = \(_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right) \) is a transition probability matrix, then at equilibrium A is equal to ________.

If  \(T=\begin{array}{l} A \\ B \end{array}\left(\begin{array}{ll} 0.7 & 0.3 \\ 0.6 & x \end{array}\right)\) is a transition probability matrix, then the value of x is ________.

Which of the following is not an elementary transformation?

If \(\left| A \right| \neq 0,\) then A is _______.

For what value of k, the matrix \(A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right) \) has no inverse?

The rank of an n x n matrix each of whose elements is 2 is __________

The value of \(\left| \begin{matrix} { 5 }^{ 2 } & { 5 }^{ 3 } & { 5 }^{ 4 } \\ { 5 }^{ 3 } & { 5 }^{ 4 } & { 5^{ 5 } } \\ { 5 }^{ 4 } & { 5 }^{ 5 } & { 5 }^{ 6 } \end{matrix} \right| \)

If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

Find the rank of each of the following matrices.
\(\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right) \)

If A=\(\left( \begin{matrix} 1 & 1 & -1 \\ 2 & -3 & 4 \\ 3 & -2 & 3 \end{matrix} \right) \) and B=\(\left( \begin{matrix} 1 & -2 & 3 \\ -2 & 4 & -6 \\ 5 & 1 & -1 \end{matrix} \right) \), then find the rank of AB and the rank of BA.

Solve the following system of equations by rank method
x + y + z = 9, 2x + 5y + 7z = 52, 2x − y − z = 0

Find the rank of the matrix \(\left[ \begin{matrix} 7 & -1 \\ 2 & 1 \end{matrix} \right] \)

Find the rank of the matrix \(\left( \begin{matrix} 2 & -4 \\ -1 & 2 \end{matrix} \right) \)

Find the rank of the matrix \(\begin{pmatrix} 1 & 5 \\ 3 & 9 \end{pmatrix}\)

Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)

Find the rank of the matrix \(\left( \begin{matrix} 0 & -1 & 5 \\ 2 & 4 & -6 \\ 1 & 1 & 5 \end{matrix} \right) \)

Find the rank of the matrix
\(A=\left( \begin{matrix} 2 & 4 & 5 \\ 4 & 8 & 10 \\ -6 & -12 & -15 \end{matrix} \right) \)

Find the rank of the matrix \(A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right) \)

Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

The following table represents the number of shares of two companies A and B during the month of January and February and it also gives the amount in rupees invested by Ravi during these two months for the purchase of shares of two companies. Find the the price per share of A and B purchased during both the months

The sum of three numbers is 6. If we multiply the third number by 2 and add the first number to the result we get 7. By adding second and third numbers to three times the first number we get 12. Find the numbers using rank method