(1 2 3
r-1
1 2 5 y
if o 2-1 7
1 0 a
a-5
0 4 7 then find the values of x, y, z and a.
1 0 0
Answers
mhhfjfhdghdhjv fidggu
Answer:
Our apps
answr
search
What would you like to ask?
12th
Maths
Determinants
Applications of Matrices and Determinants
Find the value of x,y and z...
MATHS
Find the value of x,y and z from the following equation:
(i) [
4
x
3
5
]=[
y
1
z
5
]
(ii) [
x+y
5+z
2
xy
]=[
6
5
2
8
]
(iii)
⎣
⎢
⎢
⎡
x+y+z
x+z
y+z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
9
5
7
⎦
⎥
⎥
⎤
MEDIUM
Share
Study later
VIDEO EXPLANATION
ANSWER
(i) [
4
x
3
5
]=[
y
1
z
5
]
As the given matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get: x=1,y=4, and z=3
(ii) [
x+y
5+z
2
xy
]=[
6
5
2
8
]
As the given matrices are equal, their corresponding elements are also equal. Comparing the corresponding elements, we get:
x+y=6,xy=8,5+z=5
Now, 5+z=5⇒z=0
We know that:
(x−y)
2
=(x+y)
2
−4xy
⇒(x−y)
2
=36−32=4
⇒x−y=±2
Now, when x−y=2 and x+y=6, we get x=4 and y=2
When x−y=−2 and x+y=6, we get x=2 and y=4
∴x=4,y=2 and z=0orx=2,y=4 and z=0
(iii)
⎣
⎢
⎢
⎡
x+y+z
x+z
y+z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
9
5
7
⎦
⎥
⎥
⎤
As the two matrices are equal, their corresponding elements are also equal. Comparing the corresponding elements, we get:
x+y+z=9 ....(1)
x+z=5 ....(2)
y+z=7 ....(3)
From (1) and (2), we have:
y+5=9
⇒y=4
Then, from (3), we have: 4+z=7
⇒z=3
∴x+z=5
⇒x=2
∴x=2,y=4 and z=3
Answered By
toppr
How satisfied are you with the answer?
This will help us to improve better
answr
Get Instant Solutions, 24x7
No Signup required
girl
More Questions by difficulty
EASY
MEDIUM
HARD
Prev Question
Next Question
Practice from
20+ Live Tests
and see where you stand among the best in India
Physics
Chemistry
Mathematics
Biology
Practice important Questions
NCERT Solutions for Class 12 Maths Chapter 2 & 3
130 Qs
Related Questions to study
Which of the given values of x and y make the following pairs of matrices equal?
[
3x+7
y+1
5
2−3x
] and [
0
8
y−2
4
]
Study later
View Answer
Solve each of the following system of equations in R.
x+1
4
≤3≤
x+1
6
,x>0.
Study later
View Answer
VIEW MORE
Revise with Concepts
Solving Non Homogeneous System of Linear Equations Using Matrix Method
EXAMPLE
DEFINITIONS
FORMULAES
Learn with Videos
Simultaneous Linear Equations using Matrices
Simultaneous Linear Equations using Matrices
12 min