HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`

Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`

Identify the following matrix is singular or non-singular?

`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`

Identify the following matrix is singular or non-singular?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`

Identify the following matrix is singular or non-singular?

`[(3, 5, 7),(-2, 1, 4),(3, 2, 5)]`

Identify the following matrix is singular or non-singular?

`[(7, 5),(-4, 7)]`

Find k if the following matrix is singular:

`[(7, 3),(-2, "k")]`

Find k if the following matrix is singular:

`[(4, 3, 1),(7, "k", 1),(10, 9, 1)]`

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