HSC Science (Electronics) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find k if the following matrix is singular:

`[("k" - 1, 2, 3),(3, 1, 2),(1, -2, 4)]`

If A = `[(5, 1, -1),(3, 2, 0)]`, Find (A^T)^T.

If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (A^T)^T.

Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.

The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`

The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(2, 5, 1),(-5, 4, 6),(-1, -6, 3)]`

The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`

Construct the matrix A = [a_ij]_{3 × 3} where a_ij = i − j. State whether A is symmetric or skew-symmetric.

If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, Show that A² – 4A is a scalar matrix 

If A = `[(1, 0),(-1, 7)]`, find k so that A² – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.

If A = `[(3, 1),(-1, 2)]`, prove that A² – 5A + 7I = 0, where I is unit matrix of order 2

Select the correct option from the given alternatives:

Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______

Select the correct option from the given alternatives:

If A and B are square matrices of equal order, then which one is correct among the following?

Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find B + C – A

Answer the following question:

If A = diag [2 –3 –5], B = diag [4 –6 –3] and C = diag [–3 4 1] then find 2A + B – 5C

Answer the following question:

If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.

Answer the following question:

If A = `[(1, 2, 3),(2, 4, 6),(1, 2, 3)]`, B = `[(1, -1, 1),(-3, 2, -1),(-2, 1, 0)]`, show that AB and BA are both singular matrices

Answer the following question:

If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix

If odds in favour of X solving a problem are 4:3 and odds against Y solving the same problem are 2:3. Find probability of: X solving the problem

If odds in favour of X solving a problem are 4:3 and odds against Y solving the same problem are 2:3. Find probability of: Y solving the problem