ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Matrices
Question 1
1.
    • Find A , given that A
    • +
    • 3
    • [
      1
      -1
      9
      -2
      		]
    • =
    • [
      3
      -3
      24
      -5
      		]
  • [
    0
    0
    -3
    2
    		]
  • [
    0
    -1
    -3
    1
    		]
  • [
    0
    0
    -3
    1
    		]
  • [
    0
    0
    -3
    -1
    		]
  • [
    0
    0
    -3
    4
    		]
Question 2
2.
    • The principal diagonal elements of the given matrix
    • [
      -4
      6
      -6
      7
      -1
      -8
      -3
      -9
      2
      		]
    • are
      • -6
      • ,
      • -1
      • ,
      • -3
      • -4
      • ,
      • -1
      • ,
      • 2
      • 6
      • ,
      • 7
      • ,
      • -9
      • -4
      • ,
      • -6
      • ,
      • -1
Question 3
3.
Which of the following are true for matrices A, B and C ?
a)
    • (
      A
      +
      B
      )
      ✕
      C
    • =
    • (
      A
      ✕
      B
      )
      +
      (
      A
      ✕
      C
      )
b)
    • (
      A
      ✕
      B
      )
    • =
    • (
      B
      ✕
      A
      )
c)
    • A
      ✕
      (
      B
      ✕
      C
      )
    • =
    • (
      A
      ✕
      B
      )
      ✕
      C
d)
    • (
      A
      ✕
      I
      )
    • =
    • (
      I
      ✕
      A
      )
    • = A
e)
    • (
      A
      ✕
      I
      )
    • =
    • (
      I
      ✕
      A
      )
    • = I
f)
    • A
      ✕
      (
      B
      +
      C
      )
    • =
    • (
      A
      ✕
      B
      )
      +
      (
      A
      ✕
      C
      )
  • {b,d}
  • {a,c}
  • {c,d,f}
  • {b,c,d}
  • {e,a,f}
Question 4
4.
    • The order of matrix A =
    • [
      -4
      5
      -1
      3
      -1
      2
      -2
      3
      3
      		]
    • is
  • 3 ✕ 2
  • 2 ✕ 3
  • 4 ✕ 3
  • 3 ✕ 4
  • 3 ✕ 3
Question 5
5.
Which of the following are true?
a)
If a matrix is symmetric then it is equal to its transpose
b)
A matrix is symmetric if the principal diagonal elements are same
c)
A rectangular matrix cannot be symmetric
d)
If a matrix is symmetric, then it is a square matrix
  • {a,c,d}
  • {b,a}
  • {b,a,c}
  • {b,c}
  • {b,d}
Question 6
6.
Which of the following are true for matrices A and B ?
a)
    • The orders of
    • (
      A
      ✕
      B
      )
    • and
    • (
      B
      ✕
      A
      )
    • are same
b)
    • If A and B can be multiplied, they must have the same order
c)
    • If AB = 0, A = 0 or B = 0 or both A and B are zero matrices
d)
    • If A and B can be added, they must have the same order
  • {a,d}
  • {d}
  • {b,d}
  • {c,a,d}
Question 7
7.
    • If A =
    • [
      -3
      4
      1
      3
      -4
      -3
      0
      4
      4
      		]
    • , then
    • A
      2
    • =
  • [
    21
    -24
    -11
    -21
    16
    3
    14
    0
    4
    		]
  • [
    21
    -24
    -10
    -21
    16
    3
    12
    0
    4
    		]
  • [
    21
    -24
    -11
    -21
    16
    3
    12
    0
    4
    		]
  • [
    21
    -24
    -11
    -21
    16
    3
    12
    -3
    4
    		]
  • [
    21
    -25
    -11
    -21
    16
    3
    12
    0
    4
    		]
Question 8
8.
If the elements of matrix A are multiplied with -1 , we get
  • multiplicative inverse of A
  • additive inverse of A
  • additive identity of A
  • multiplicative identity of A
Question 9
9.
    • If A =
    • [
      1
      -2
      -1
      1
      0
      0
      		]
    • and B =
    • [
      1
      2
      -1
      -2
      0
      -2
      		]
    • , then A
    • ✕
    • B =
  • [
    3
    -3
    -2
    -2
    2
    0
    -1
    1
    0
    		]
  • [
    3
    6
    1
    2
    		]
  • [
    3
    8
    1
    2
    		]
  • [
    3
    -2
    -1
    -3
    2
    1
    -2
    0
    0
    		]
  • [
    5
    8
    1
    2
    		]
Question 10
10.
    • If A =
    • [
      3
      1
      3
      0
      1
      -1
      -2
      -2
      -2
      		]
    • and B =
    • [
      -2
      -2
      1
      -1
      0
      1
      1
      -1
      -2
      		]
    • , then A
    • ✕
    • B =
  • [
    -4
    -11
    -2
    -2
    1
    3
    4
    6
    0
    		]
  • [
    -4
    -9
    -2
    -2
    1
    3
    4
    6
    0
    		]
  • [
    -4
    -9
    -2
    -1
    1
    3
    4
    6
    0
    		]
  • [
    -4
    -9
    -2
    -2
    1
    3
    7
    6
    0
    		]
  • [
    -4
    -9
    -2
    -2
    1
    3
    4
    6
    -1
    		]