S.T DANIEL COMBONI SECONDARY SCHOOL HAWASSA
2023/24
2016E.C WORK SHEET 3 ON MATRICES FOR GRADE 11
1995/58.Let A,B and C be 2 × 2 matrices where the entries are real numbers. Which of the following is always true ?
A) A.B= B. A
C) If A.B=A.C, then B = C
0 0
0 0
1 0
B) If A ≠
, then B ≠
D) If A =
, then A. B = B. A
0 0
0 0
0 1
𝑥
2
−1
1995/59. Which of the following is the set of all values of 𝑥 so that the matrix 1 𝑥 − 1 1 is invertible?
0
1
2
5
3
A) 1
B) – 1,2
C) – 1, 2
D) 2 , 1
1 2
1995/61. Let A =
, which of the following is true?(Note (I,j) entry means the
3 4
th
th
i row and j column)
−1
A) The 1,1 entry of A−1 is 2
C) The 2,1 entry of A−1 is
−1
−1
3
2
2
B) The 1,2 entry of A is 1
D) The 2,2 entry of A is
1
4 0
2 2
2003/62. Suppose A =
and B =
.If X is a 2 × 2matrixsuch that X + 2 B T = A. B , then X isequal to :
1 1
6 −4
7 5
5 −3
5 −3
7 5
A)
B)
C)
D)
5 4
5 0
5 2
7 0
2 7
1 1
−1
−1
2003/64 . If A =
and B =
, then A. B
is equal to
1 3
0 2
−3 11
4 −3
4 0
−2 5
A)
B)
C)
D)
1 −3
4 −5
0 2
2 −4
𝑥 − 𝑦 − 2𝑧 = 0
2003/65. Which of the following is the solution set of −2𝑥 + 6𝑧 = 1
?
−𝑥 + 2𝑦 + 𝑧 = 1
A) 1,0.0,5
B)
3𝑡 + 1,0, 𝑡 : 𝑡 ∈ ℝ
C) ℝ3
D) ∅
1
−1
0
3 such that A + 2B T = 0.
1−x 2
Then which of the following is the value of y ?
13
A) 0
B) − 2
C) – 8
D) any real number
𝑥 + 𝑦 + 3𝑧 = 1
𝑥 + 2𝑦 + 𝑧 = 2
2004/21. What is the solution set of the following system of equation
?
−2𝑥 − 2𝑦 − 4𝑧 = −2
A) 0,1,0 B) −∞. ∞ C) – 3𝑘, 𝑘 + 1. 𝑘 ; 𝑘 ∈ ℝ D) 𝑘, 𝑘 − 1, 𝑘 ; 𝑘𝜖ℝ
1 2
2005/7. Suppose 𝐴 =
. If X is a 2 × 2 matrix such that 𝐴𝑋 − 𝐴𝑇 = 2𝐴 , then what is the value of X ?
2 3
3 1
3 3
3 6
3 0
A)
B)
C)
D)
1 3
3 3
6 0
0 3
2004/19. Let A =
−2
0
x
and B =
2y x + y −4
2 0 −1
2006/2 If A= 1 2 0 and 2A + B T = AT A ,then which one of the following is
0 0 −1
1 0 −2
0 0 0
2 0 −4
1 2
A) 2 0 0 B) 0 0 0
C) 4 8 0
D) 0 0
0 0 4
0 0 0
0 0 −4
−2 0
equal to B?
0
0
4
2006/22 What should be the value of k so that the system of equation
x−y =z=1
−x + 5y − 4z = 1has a solution ?
2x + 2y − z = k
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S.T DANIEL COMBONI SECONDARY SCHOOL HAWASSA
2023/24
A) 0
B) 1
C) −4
D) 4
0 x
0
1 1 1
2007/37. If A = 1 −1 1 and A−1 = 3 0 0 , then what are the values of x and y ?
0 y −1
2 0 −1
2
1
1
2
A) 𝑥 = 3 , 𝑦 = −2 B) 𝑥 = 3 , 𝑦 = 3 C) x = −3 , y = 2
D) x = 3 and y = 3
2007/41. What is the solution set of the system
x+y−z=1
x + 2y − 3z = 1 ?
2x + 3y − 4z = 2
0,2,1
B) 1 − k, 2k, k
C) 2k + 1, −k, k
D) ∅
2 7
1 1
−1
−1
2008/13. If A =
and B =
, then A. B
is equal to :
1 3
0 2
4 −3
−3 11
4 0
−2 5
A)
B)
C)
D)
4 −5
1 −3
0 2
2 −4
𝑥 − 3𝑦 − 2𝑧 = 6
2008/38. The solution of the system of linear equation of 2𝑥 − 4𝑦 − 3𝑧 = 8 is:
−3𝑥 + 6𝑦 + 8𝑧 = −5
A)
A) 𝑥 = −1, 𝑦 = −3, 𝑧 = −2
B) 𝑥 = −1, 𝑦 = −3, 𝑧 = 2
1 1 0
2008/34. The inverse of a matrix 1 1 1 is :
0 2 1
1
1 −1
1 1 2
1
1
A) 2 1 −1 1
B) − 2 −1 1 2
−2 2
0
1 −1 0
C) 𝑥 = 1, 𝑦 = −3, 𝑧 = 2
D) 𝑥 = 1, 𝑦 = 3, 𝑧 = −2
C)
1
2
−1 −1 −1
− 1 −1 −2
1 −1 0
D)
1
2
1 1 2
−1 1 2
1 −1 0
x + y + 2z = 1
2008/43. What is the solution set of the system x + 2y + z = 1 ?
3x + 4y + 5z = 3
C) −3k + 1, k, k
D) ∅
x − 2y + z = 1
2011/16. Consider the following system of equations −x + y + z = 3 . How much
3x − 5y + z = k
must be the value of k so that the system has a solution ?
A) 7
B) 1
C) 0
D) −1
x 2x
−1 −2
2012/25. If the inverse of the matrix
is
, then which one of the following is the value of x?
−x x
1
1
1
1
A) – 1
B) 1
C) −
D)
A)
1,0.0
B)
k + 1, −k, 0
3
2012/26. What is the value of k so that the system
A) ℝ
B) ℝ ∖ 1
3
x − 2y + z = 3
2x + y − z = 4 ,has unique solution:
kx − 2y − z = 5
C) ℝ ∖ −1
D) )ℝ ∖ −1,1
1 2
2 −1
and B =
. Then which of the following is equal to 3A + 2B ?
4 3
−1 3
7 4
7 1
3 1
3 4
A)
B)
C)
D)
7 18
7 7
2 7
2 18
2012/27. Let A =
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S.T DANIEL COMBONI SECONDARY SCHOOL HAWASSA
2013/ 27.Which of the following is the product of A.B of the two matrices
A=
2023/24
−2 3
−1 5
and B =
?
1 4
3 0
−11 10
−11 −10
−11 10
11 −10
B)
C)
D)
11
5
11
5
11 −5
11
5
2 3
2013/29. Which of the following is the inverse of the
?
3 4
−2 3
−4 3
−4 −3
4 −3
A
B)
C)
D)
3 −4
3 −2
−3 −2
−3 2
0 −1
2014/3. LetA =
. Which one of the following is equal to A + AT ?
5 1
0 4
0 −4
0 −5
0 5
A)
B)
C)
D)
4 2
−4 2
−5 −1
5 1
1 3 0
2 0 5
2014/7. Given matrices A = 3 1 4 and B = 6 5 2 , Which one of the
9 7 0
0 6 −2
following𝑖𝑠 A − B ? =
1 −3 5
1
3
5
1 −3 −5
A) −3 −4 2
B −3 −4 −2
C) = −3 −4 2
−9 −1 −2
−9 1
2
9
1
2
A)
D)
1
3 5
−3 −4 2
9
1 2
2𝑥 + 𝑦 + 3𝑧 = 4
𝑥−𝑧 =1
2014/23. Which one of the following is the augmented matrix associated to the system of equations
−4𝑥 + 𝑦 − 3 = 0
3
2
1 1
3 1 2 4
1
2
3 4
2 1 3 4
A) −1 1 −1 3
B) −1 0 1 1
C) −1 1 −1 1
D) 1 0 −1 1
−1 −4 1 4
−4 1 −3 0
1 −4 −1 3
−4 1 0 3
−𝑥 − 𝑦 − 𝑦 = 10
2015/8. Consider the system of equations 7𝑥 + 𝑦 − 2𝑧 = −1 , which one of the following is the correct augmented
6𝑥 − 2𝑦 + 4𝑧 = 7
matrix of the given system ?
−1 7
6
−1 −1 −1 10
−1
1
−2
A)
C) 7
1 −2−1
−1 −2 4
6
−2
4 7
10 −1 7
10 −1 −1−1
B) −1 −2 1 7
7
4 −2 6
2015/10. Let 𝑀 =
1
2
−1
2
−1
2
1
2
and 𝑄 =
D)
?
−1 −1 −1
7
1 −2
6 −2 4
10 −1 7
1 −1
be given matrices. Which one of the following is true ?
−1 1
3
1
A) 2Q = M
B) 3M = 2 Q
C) 2M = −Q
D) 2 Q = 2M
2 −1
3
1
1 𝑏
2015/37 . If
=
. The what are the values of 𝑎 and 𝑏 respectively ?
𝑎 4
−1 18
−1 3
A)2, −2
B)3,2
C)0, −1
D)−1,2
1 −1
2015/38.Let = 0
2 . Then AT is:
−3 6
1 0
−1 1
1 0 −3
−1 2 6
A) −1 2
B)
C) 2
D)−
0
−1 2 6
1 0 −3
−3 6
6 −3
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