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Algebra

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Matrices: Concept, Types, Transpose, Symmetric and Skew-symmetric matrices

Subtopic

Matrices: Concept, Types, Transpose, Symmetric and Skew-symmetric matrices under Algebra for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the result of A+AA + A if AA is a skew-symmetric matrix?

    A.

    A symmetric matrix

    B.

    A skew-symmetric matrix

    C.

    An identity matrix

    D.

    A zero matrix

  2. 2.

    If AA is a square matrix such that AT=AA^T = A, then AA is called:

    A.

    Diagonal

    B.

    Skew-symmetric

    C.

    Symmetric

    D.

    Scalar

  3. 3.

    The diagonal elements of a matrix A=[aij]A = [a_{ij}] are those for which:

    A.

    i<ji < j

    B.

    i>ji > j

    C.

    i=ji = j

    D.

    i+j=0i + j = 0

Download the worksheet for Algebra - Matrices: Concept, Types, Transpose, Symmetric and Skew-symmetric matrices to practice offline. It includes additional chapter-level practice questions.

Operations on Matrices: Addition, Multiplication, Scalar Multiplication

Subtopic

Operations on Matrices: Addition, Multiplication, Scalar Multiplication under Algebra for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the product [45][10]\begin{bmatrix} 4 & 5 \end{bmatrix} \begin{bmatrix} 1 \\ 0 \end{bmatrix}.

    A.

    [4]\begin{bmatrix} 4 \end{bmatrix}

    B.

    [5]\begin{bmatrix} 5 \end{bmatrix}

    C.

    [40]\begin{bmatrix} 4 & 0 \end{bmatrix}

    D.

    [45]\begin{bmatrix} 4 \\ 5 \end{bmatrix}

  2. 2.

    If AA and BB are square matrices of the same order, then k(A+B)k(A + B) is equal to:

    A.

    kA+BkA + B

    B.

    A+kBA + kB

    C.

    kA+kBkA + kB

    D.

    k2(A+B)k^2(A + B)

  3. 3.

    Find the result of [2003][1001]\begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix} \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}.

    A.

    [1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

    B.

    [2003]\begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix}

    C.

    [3004]\begin{bmatrix} 3 & 0 \\ 0 & 4 \end{bmatrix}

    D.

    [0000]\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}

Download the worksheet for Algebra - Operations on Matrices: Addition, Multiplication, Scalar Multiplication to practice offline. It includes additional chapter-level practice questions.

Determinants: Properties, Minors, Co-factors

Subtopic

Determinants: Properties, Minors, Co-factors under Algebra for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the co-factor C22C_{22} in the determinant āˆ£123040567āˆ£\begin{vmatrix} 1 & 2 & 3 \\ 0 & 4 & 0 \\ 5 & 6 & 7 \end{vmatrix}?

    A.

    -8

    B.

    8

    C.

    -15

    D.

    15

  2. 2.

    Find the value of āˆ£secā”2Īøtanā”2Īø11āˆ£\begin{vmatrix} \sec^2 \theta & \tan^2 \theta \\ 1 & 1 \end{vmatrix}.

    A.

    0

    B.

    1

    C.

    -1

    D.

    2

  3. 3.

    If Ī”=āˆ£1234āˆ£\Delta = \begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}, then Ī”\Delta is equal to which of the following?

    A.

    āˆ£3412āˆ£\begin{vmatrix} 3 & 4 \\ 1 & 2 \end{vmatrix}

    B.

    āˆ’āˆ£3412āˆ£-\begin{vmatrix} 3 & 4 \\ 1 & 2 \end{vmatrix}

    C.

    āˆ£2143āˆ£\begin{vmatrix} 2 & 1 \\ 4 & 3 \end{vmatrix}

    D.

    0

Download the worksheet for Algebra - Determinants: Properties, Minors, Co-factors to practice offline. It includes additional chapter-level practice questions.

Adjoint and Inverse of a Matrix

Subtopic

Adjoint and Inverse of a Matrix under Algebra for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If A=[4131]A = \begin{bmatrix} 4 & 1 \\ 3 & 1 \end{bmatrix}, what is the value of āˆ£Aāˆ’1āˆ£|A^{-1}|?

    A.

    1

    B.

    4

    C.

    7

    D.

    1/1

  2. 2.

    If AA is a square matrix of order 2 and āˆ£Aāˆ£=5|A| = 5, then āˆ£adj(adjA)āˆ£|adj(adj A)| is:

    A.

    5

    B.

    25

    C.

    1

    D.

    125

  3. 3.

    If A=[100010001]A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, then adjAadj A is:

    A.

    [100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

    B.

    [000000000]\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}

    C.

    [āˆ’1000āˆ’1000āˆ’1]\begin{bmatrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \end{bmatrix}

    D.

    [300030003]\begin{bmatrix} 3 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 3 \end{bmatrix}

Download the worksheet for Algebra - Adjoint and Inverse of a Matrix to practice offline. It includes additional chapter-level practice questions.

Solving system of linear equations using matrix method

Subtopic

Solving system of linear equations using matrix method under Algebra for Grade 12 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    In the matrix form of x+y+z=1x + y + z = 1, x+y+z=2x + y + z = 2, x+y+z=3x + y + z = 3, the matrix AA would be:

    A.

    [111111111]\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}

    B.

    [123123123]\begin{bmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \\ 1 & 2 & 3 \end{bmatrix}

    C.

    [100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

    D.

    [xyz]\begin{bmatrix} x \\ y \\ z \end{bmatrix}

  2. 2.

    Which of the following matrices has no inverse?

    A.

    [1112]\begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}

    B.

    [1236]\begin{bmatrix} 1 & 2 \\ 3 & 6 \end{bmatrix}

    C.

    [4512]\begin{bmatrix} 4 & 5 \\ 1 & 2 \end{bmatrix}

    D.

    [1001]\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

  3. 3.

    If A=[3102]A = \begin{bmatrix} 3 & 1 \\ 0 & 2 \end{bmatrix}, then āˆ£Aāˆ£|A| is:

    A.

    5

    B.

    6

    C.

    3

    D.

    2

Download the worksheet for Algebra - Solving system of linear equations using matrix method to practice offline. It includes additional chapter-level practice questions.