HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Choose the correct alternative:

If p(A) = r then which of the following is correct?

Choose the correct alternative:

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

Choose the correct alternative:

If the rank of the matrix `[(lambda, -1, 0),(0, lambda, -1),(-1, 0, lambda)]` is 2, then λ is

Choose the correct alternative:

The rank of the diagonal matrix `[(1, , , , ,),(, 2, , , ,),(, , -3, , ,),(, , , 0, ,),(, , , , 0,),(, ,  , , ,0)]`

Choose the correct alternative:

Which of the following is not an elementary transformation?

Choose the correct alternative:

If p(A) = p(A,B)= then the system is

Choose the correct alternative:

If p(A) = p(A, B)= the number of unknowns, then the system is

Choose the correct alternative:

If p(A) ≠ p(A, B) =, then the system is

Choose the correct alternative:

If the number of variables in a non-homogeneous system AX = B is n, then the system possesses a unique solution only when

Choose the correct alternative:

The system of equations 4x + 6y = 5, 6x + 9y = 7 has

Choose the correct alternative:

For the system of equations x + 2y + 3z = 1, 2x + y + 3z = 3, 5x + 5y + 9z = 4

Choose the correct alternative:

If |A| ≠ 0, then A is

Choose the correct alternative:

The system of linear equations x = y + z = 2, 2x + y – z = 3, 3x + 2y + k = 4 has unique solution, if k is not equal to

Choose the correct alternative:

If `|"A"_("n" xx "n")|` = 3 and |adj A| = 243 then the value n is

Choose the correct alternative:

Rank of a null matrix is

Find the rank of the matrix

A = `((1, -3, 4, 7),(9, 1, 2, 0))`

Find the rank of the matrix

A = `((-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7))`

Find the rank of the matrix

A = `((4, 5, 2, 2),(3, 2, 1, 6),(4, 4, 8, 0))`

Examine the consistency of the system of equations:

x + y + z = 7, x + 2y + 3z = 18, y + 2z = 6

Find k if the equations 2x + 3y – z = 5, 3x – y + 4z = 2, x + 7y – 6z = k are consistent