ICSE Board Practice

ICSE Grade X - Matrices
Question 1
1.
    • If A =
    • [
      0
      -3
      -2
      3
      ]
    • and B =
    • [
      -2
      4
      3
      0
      ]
    • , then
    • 3
    • A
    • +
    • 10
    • B =
  • [
    -20
    31
    23
    9
    ]
  • [
    -20
    31
    24
    9
    ]
  • [
    -20
    31
    26
    9
    ]
  • [
    -20
    31
    24
    10
    ]
  • [
    -20
    31
    21
    9
    ]
Question 2
2.
    • The order of matrix A =
    • [
      3
      -3
      2
      3
      4
      0
      ]
    • is
  • 3 ✕ 3
  • 4 ✕ 2
  • 2 ✕ 2
  • 2 ✕ 3
  • 3 ✕ 2
Question 3
3.
    • Which of the following matrices is a
    • 2 ✕ 1
    • matrix ?
  • [
    4
    9
    4
    2
    1
    5
    ]
  • [
    3
    5
    7
    9
    ]
  • [
    2
    2
    ]
  • [
    5
    1
    6
    ]
  • [
    1
    7
    ]
Question 4
4.
    • If A =
    • [
      8
      4
      -8
      6
      ]
    • , then find B satisfying A
    • ✕ B = A
  • [
    1
    0
    0
    1
    ]
  • [
    4
    0
    0
    1
    ]
  • [
    2
    0
    0
    1
    ]
  • [
    1
    0
    0
    -2
    ]
  • [
    1
    -1
    0
    1
    ]
Question 5
5.
    • If A =
    • [
      -2
      1
      4
      -1
      1
      -3
      0
      -1
      -1
      ]
    • , then
    • 10
    • A =
  • [
    -20
    10
    40
    -10
    13
    -30
    0
    -10
    -10
    ]
  • [
    -20
    10
    40
    -10
    10
    -30
    1
    -10
    -10
    ]
  • [
    -20
    10
    40
    -10
    10
    -30
    0
    -10
    -10
    ]
  • [
    -20
    10
    40
    -10
    8
    -30
    0
    -10
    -10
    ]
  • [
    -21
    10
    40
    -10
    10
    -30
    0
    -10
    -10
    ]
Question 6
6.
    • If A =
    • [
      a

      11
      a

      12
      a

      13
      a

      21
      a

      22
      a

      23
      a

      31
      a

      32
      a

      33
      ]
    • and B =
    • [
      b

      11
      b

      12
      b

      13
      b

      21
      b

      22
      b

      23
      b

      31
      b

      32
      b

      33
      ]
    • ,
    • then
    • (
      A
      B
      )
    • =
  • [
    a

    11
       
    b

    11
    a

    12
       
    b

    12
    a

    13
       
    b

    13
    a

    21
       
    b

    21
    a

    22
       
    b

    22
    a

    23
       
    b

    23
    a

    31
       
    b

    31
    a

    32
       
    b

    32
    a

    33
       
    b

    33
    ]
  • [
    a

    11
       
    b

    11
    a

    21
       
    b

    21
    a

    31
       
    b

    31
    a

    12
       
    b

    12
    a

    22
       
    b

    22
    a

    32
       
    b

    32
    a

    13
       
    b

    13
    a

    23
       
    b

    23
    a

    33
       
    b

    33
    ]
  • [
    a

    11
       
    b

    11
    a

    21
       
    b

    12
    a

    31
       
    b

    13
    a

    12
       
    b

    21
    a

    22
       
    b

    22
    a

    32
       
    b

    23
    a

    13
       
    b

    31
    a

    23
       
    b

    32
    a

    33
       
    b

    33
    ]
  • [
    a

    11
    b

    11
      +  
    a

    12
    b

    21
      +  
    a

    13
    b

    31
    a

    11
    b

    12
      +  
    a

    12
    b

    22
      +  
    a

    13
    b

    32
    a

    11
    b

    13
      +  
    a

    12
    b

    23
      +  
    a

    13
    b

    33
    a

    21
    b

    11
      +  
    a

    22
    b

    21
      +  
    a

    23
    b

    31
    a

    21
    b

    12
      +  
    a

    22
    b

    22
      +  
    a

    23
    b

    32
    a

    21
    b

    13
      +  
    a

    22
    b

    23
      +  
    a

    23
    b

    33
    a

    31
    b

    11
      +  
    a

    32
    b

    21
      +  
    a

    33
    b

    31
    a

    31
    b

    12
      +  
    a

    32
    b

    22
      +  
    a

    33
    b

    32
    a

    31
    b

    13
      +  
    a

    32
    b

    23
      +  
    a

    33
    b

    33
    ]
Question 7
7.
    • If A =
    • [
      1
      1
      6
      2
      ]
    • and B =
    • [
      2
      6
      7
      8
      ]
    • , find
    • (
      A
      +
      B
      )
      2
       
  • [
    103
    91
    169
    191
    ]
  • [
    100
    88
    169
    191
    ]
  • [
    100
    91
    169
    192
    ]
  • [
    100
    91
    169
    190
    ]
  • [
    100
    91
    169
    191
    ]
Question 8
8.
    • If A =
    • [
      a

      11
      a

      12
      a

      21
      a

      22
      ]
    • and B =
    • [
      b

      11
      b

      12
      b

      21
      b

      22
      ]
    • ,
    • then
    • (
      A
      +
      B
      )
    • =
  • [
    a

    11
    b

    11
      +  
    a

    12
    b

    21
    a

    11
    b

    12
      +  
    a

    12
    b

    22
    a

    21
    b

    11
      +  
    a

    22
    b

    21
    a

    21
    b

    12
      +  
    a

    22
    b

    22
    ]
  • [
    a

    11
      +  
    b

    11
    a

    12
      +  
    b

    12
    a

    21
      +  
    b

    21
    a

    22
      +  
    b

    22
    ]
  • [
    a

    11
      +  
    b

    11
    a

    21
      +  
    b

    21
    a

    12
      +  
    b

    12
    a

    22
      +  
    b

    22
    ]
  • [
    a

    11
      +  
    b

    11
    a

    21
      +  
    b

    12
    a

    12
      +  
    b

    21
    a

    22
      +  
    b

    22
    ]
Question 9
9.
    • Which of the following matrices is a
    • 1 ✕ 2
    • matrix ?
  • [
    1
    6
    6
    ]
  • [
    7
    3
    6
    7
    ]
  • [
    4
    7
    5
    7
    2
    3
    ]
  • [
    3
    4
    ]
  • [
    5
    1
    ]
Question 10
10.
    • If A =
    • [
      -1
      3
      1
      3
      ]
    • , then find B satisfying A
    • +
    • B = I
  • [
    2
    -1
    -1
    -2
    ]
  • [
    2
    -3
    -1
    -3
    ]
  • [
    2
    -3
    -1
    -2
    ]
  • [
    2
    -2
    -1
    -2
    ]
  • [
    2
    -5
    -1
    -2
    ]