## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 8 Matrices Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 8 Matrices Chapter Test

More Exercises

Question 1.
Find the values of a and below
$$\begin{bmatrix} a+3 & { b }^{ 2 }+2 \\ 0 & -6 \end{bmatrix}=\begin{bmatrix} 2a+1 & 3b \\ 0 & { b }^{ 2 }-5b \end{bmatrix}$$
Solution:
$$\begin{bmatrix} a+3 & { b }^{ 2 }+2 \\ 0 & -6 \end{bmatrix}=\begin{bmatrix} 2a+1 & 3b \\ 0 & { b }^{ 2 }-5b \end{bmatrix}$$
comparing the corresponding elements
a + 3 = 2a + 1
⇒ 2a – a =3 – 1
⇒ a = 2
b² + 2 = 3b
⇒ b² – 3b + 2 = 0
⇒ b² – b – 2b + 2 = 0
⇒ b (b – 1) – 2 (b – 1) = 0
⇒ (b – 1) (b – 2) = 0.
Either b – 1 = 0, then b = 1
or b – 2 = 0, then b = 2
Hence a = 2, b = 2 or 1

Question 2.
Find a, b, c and d if $$3\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 4 & a+b \\ c+d & 3 \end{bmatrix}+\begin{bmatrix} a & 6 \\ -1 & 2d \end{bmatrix}$$
Solution:
Given
$$3\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 4 & a+b \\ c+d & 3 \end{bmatrix}+\begin{bmatrix} a & 6 \\ -1 & 2d \end{bmatrix}$$

Question 3.
Find X if Y = $$\begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$$ and 2X + Y = $$\begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix}$$
Solution:
Given
2X + Y = $$\begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix}$$
⇒ 2X = 2X + Y = $$\begin{bmatrix} 1 & 0 \\ -3 & 2 \end{bmatrix}$$ – Y

Question 4.
Determine the matrices A and B when
A + 2B = $$\begin{bmatrix} 1 & 2 \\ 6 & -3 \end{bmatrix}$$ and 2A – B = $$\begin{bmatrix} 2 & -1 \\ 2 & -1 \end{bmatrix}$$
Solution:
A + 2B = $$\begin{bmatrix} 1 & 2 \\ 6 & -3 \end{bmatrix}$$ …..(i)
2A – B = $$\begin{bmatrix} 2 & -1 \\ 2 & -1 \end{bmatrix}$$ …….(ii)
Multiplying (i) by 1 and (ii) by 2

Question 5.
(i) Find the matrix B if A = $$\begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}$$ and A² = A + 2B
(ii) If A = $$\begin{bmatrix} 1 & 2 \\ -3 & 4 \end{bmatrix}$$, B = $$\begin{bmatrix} 0 & 1 \\ -2 & 5 \end{bmatrix}$$
and C = $$\begin{bmatrix} -2 & 0 \\ -1 & 1 \end{bmatrix}$$ find A(4B – 3C)
Solution:
A = $$\begin{bmatrix} 4 & 1 \\ 2 & 3 \end{bmatrix}$$
let B = $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$

Question 6.
If A = $$\begin{bmatrix} 1 & 4 \\ 1 & 0 \end{bmatrix}$$, B = $$\begin{bmatrix} 2 & 1 \\ 3 & -1 \end{bmatrix}$$ and C = $$\begin{bmatrix} 2 & 3 \\ 0 & 5 \end{bmatrix}$$ compute (AB)C = (CB)A ?
Solution:
Given
A = $$\begin{bmatrix} 1 & 4 \\ 1 & 0 \end{bmatrix}$$,
B = $$\begin{bmatrix} 2 & 1 \\ 3 & -1 \end{bmatrix}$$ and
C = $$\begin{bmatrix} 2 & 3 \\ 0 & 5 \end{bmatrix}$$

Question 7.
If A = $$\begin{bmatrix} 3 & 2 \\ 0 & 5 \end{bmatrix}$$ and B = $$\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix}$$ find the each of the following and state it they are equal:
(i) (A + B)(A – B)
(ii)A² – B²
Solution:
Given
A = $$\begin{bmatrix} 3 & 2 \\ 0 & 5 \end{bmatrix}$$ and
B = $$\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix}$$

Question 8.
If A = $$\begin{bmatrix} 3 & -5 \\ -4 & 2 \end{bmatrix}$$ find A² – 5A – 14I
Where I is unit matrix of order 2 x 2
Solution:
Given
A = $$\begin{bmatrix} 3 & -5 \\ -4 & 2 \end{bmatrix}$$

Question 9.
If A = $$\begin{bmatrix} 3 & 3 \\ p & q \end{bmatrix}$$ and A² = 0 find p and q
Solution:
Given
A = $$\begin{bmatrix} 3 & 3 \\ p & q \end{bmatrix}$$

Question 10.
If A = $$\begin{bmatrix} \frac { 3 }{ 5 } & \frac { 2 }{ 5 } \\ x & y \end{bmatrix}$$ and A² = I, find x,y
Solution:
Given
A = $$\begin{bmatrix} \frac { 3 }{ 5 } & \frac { 2 }{ 5 } \\ x & y \end{bmatrix}$$

Question 11.
If $$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$$ find a,b,c and d
Solution:
Given
$$\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}\begin{bmatrix} a & b \\ c & d \end{bmatrix}=\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$$

Question 12.
Find a and b if
$$\begin{bmatrix} a-b & b-4 \\ b+4 & a-2 \end{bmatrix}\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}=\begin{bmatrix} -2 & -2 \\ 14 & 0 \end{bmatrix}$$
Solution:
Given
$$\begin{bmatrix} a-b & b-4 \\ b+4 & a-2 \end{bmatrix}\begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix}=\begin{bmatrix} -2 & -2 \\ 14 & 0 \end{bmatrix}$$

Question 13.
If A = $$\begin{bmatrix} { sec60 }^{ o } & { cos90 }^{ o } \\ { -3tan45 }^{ o } & { sin90 }^{ o } \end{bmatrix}$$ and B = $$\begin{bmatrix} 0 & { cos45 }^{ o } \\ -2 & { 3sin90 }^{ o } \end{bmatrix}$$
Find (i) 2A – 3B (ii) A² (iii) BA
Solution:
Given
A = $$\begin{bmatrix} { sec60 }^{ o } & { cos90 }^{ o } \\ { -3tan45 }^{ o } & { sin90 }^{ o } \end{bmatrix}$$ and
B = $$\begin{bmatrix} 0 & { cos45 }^{ o } \\ -2 & { 3sin90 }^{ o } \end{bmatrix}$$

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 8 Matrices Chapter Test are helpful to complete your math homework.

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