ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Matrices
Question 1
1.
Which of the following are true for matrices A and B ?
a)
    • If A and B can be added, they must have the same order
b)
    • If AB = 0, A = 0 or B = 0 or both A and B are zero matrices
c)
    • The orders of
    • (
      A
      ✕
      B
      )
    • and
    • (
      B
      ✕
      A
      )
    • are same
d)
    • If A and B can be multiplied, they must have the same order
  • {b,a}
  • {d,b,a}
  • {c,a}
  • {a}
Question 2
2.
    • Which of the following matrices can be added to
    • [
      1
      4
      4
      1
      		]
    • ?
  • [
    9
    9
    3
    1
    		]
  • [
    8
    2
    7
    4
    3
    6
    5
    7
    9
    3
    5
    2
    		]
  • [
    9
    3
    		]
  • [
    7
    2
    6
    5
    5
    9
    		]
  • [
    8
    9
    9
    5
    3
    6
    		]
Question 3
3.
    • Matrix A =
    • [
      -2
      -1
      3
      1
      -3
      -1
      -2
      4
      4
      		]
    • is the additive inverse of
  • [
    2
    1
    -3
    -1
    3
    -2
    2
    -4
    -4
    		]
  • [
    2
    1
    -3
    -1
    4
    1
    2
    -4
    -4
    		]
  • [
    2
    1
    -3
    -1
    3
    1
    2
    -2
    -4
    		]
  • [
    2
    1
    -3
    -1
    3
    1
    2
    -4
    -4
    		]
  • [
    2
    0
    -3
    -1
    3
    1
    2
    -4
    -4
    		]
Question 4
4.
    • Find
    • [
      x
      y
      		]
    • [
      a
      b
      c
      d
      		]
    • [
      x
      y
      		]
  • [
    x
    2
    a
    		  +  
    y
    b
    x
    		  +  
    x
    c
    y
    		  +  
    y
    2
    d
    		]
  • [
    x
    2
    a
    		  +  
    x
    y
    c
    x
    2
    b
    		  +  
    x
    y
    d
    y
    x
    a
    		  +  
    y
    2
    c
    y
    x
    b
    		  +  
    y
    2
    d
    		]
  • [
    x
    2
    		  +  
    y
    2
    		]
  • [
    x
    2
    a
    		  +  
    y
    c
    x
    		  +  
    x
    b
    y
    		  +  
    y
    2
    d
    		]
  • [
    x
    a
    y
    		  +  
    y
    2
    b
    		  +  
    x
    2
    c
    		  +  
    y
    d
    x
    		]
Question 5
5.
    • If A and B are given as below, neither
    • (
      A
      ✕
      B
      )
    • nor
    • (
      B
      ✕
      A
      )
    • is possible for which of the following pairs?
      • 3 ✕ 1 , 1 ✕ 3
      • 1 ✕ 2 , 2 ✕ 3
      • 2 ✕ 2 , 3 ✕ 3
      • 1 ✕ 2 , 2 ✕ 1
      • 2 ✕ 3 , 3 ✕ 1
Question 6
6.
    • If A =
    • [
      -1
      -2
      -1
      0
      		]
    • and B =
    • [
      -3
      -5
      6
      5
      		]
    • , then
    • 7
    • A
    • −
    • 10
    • B =
  • [
    23
    36
    -66
    -50
    		]
  • [
    23
    36
    -67
    -50
    		]
  • [
    23
    36
    -67
    -47
    		]
  • [
    23
    36
    -70
    -50
    		]
  • [
    23
    36
    -68
    -50
    		]
Question 7
7.
    • If A =
    • [
      0
      8
      -7
      -8
      		]
    • , B =
    • [
      1
      -1
      -2
      7
      		]
    • and C =
    • [
      7
      -8
      -6
      -7
      		]
    • ,
    • then compute
    • A
      2
    • +
    • BC =
  • [
    -42
    -65
    0
    -25
    		]
  • [
    -46
    -65
    0
    -25
    		]
  • [
    -43
    -65
    0
    -25
    		]
  • [
    -43
    -66
    0
    -25
    		]
  • [
    -43
    -65
    0
    -23
    		]
Question 8
8.
    • If A =
    • [
      0
      -2
      -2
      2
      		]
    • , then find B satisfying A
    • +
    • B = I
  • [
    1
    2
    2
    -1
    		]
  • [
    3
    2
    2
    -1
    		]
  • [
    1
    2
    2
    -2
    		]
  • [
    -2
    2
    2
    -1
    		]
  • [
    2
    2
    2
    -1
    		]
Question 9
9.
    • Which of the following matrices is comparable to the
    • given matrix
    • [
      7
      8
      4
      8
      		]
    • ?
  • [
    9
    5
    9
    1
    		]
  • [
    7
    2
    2
    7
    6
    2
    2
    6
    6
    9
    5
    3
    		]
  • [
    5
    2
    9
    9
    9
    3
    		]
  • [
    4
    2
    		]
  • [
    6
    1
    3
    3
    8
    6
    		]
Question 10
10.
    • The number of columns in matrix A =
    • [
      -9
      -3
      -9
      -9
      		]
    • is
  • 1
  • 4
  • 2
  • 3
  • 0