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Find X, Y, Z And T, If `3[[X Y],[Z T]]=[[X 6],[-1 2t]]+[[4 X+Y],[Z+T 3]]` - Mathematics

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Question

Find xyz and t, if

`3[[x     y],[z      t]]=[[x        6],[-1          2t]]+[[4             x+y],[z+t         3]]`

 

Sum

Solution

`3 [[x    y],[z    t]]=[[x       6],[-1      2t]]+[[4           x+y],[z+t        3]]`

`⇒ [[3x      3y],[3z       3t]]` = `[[x+ 4           6+x+y],[-1+z+t            2t+3]]`

∴ 3x=x+4  

⇒3x−x=4 

⇒2x=4     

⇒x=2

Also,

3y=6+x+y

⇒3y−y=6+x

⇒2y=6+x             ...(1)

Putting the value of x in eq. (1), we get

2y=6+2

⇒2y=8 

⇒y=4

Now,

3t=2t+3

⇒3t−2t=3

⇒t=3

3z=−1+z+t 

⇒3z−z=−1+t

⇒2z=−1+t             ...(2)  

Putting the value of t in eq. (2), we get

2z=−1+3

⇒2z=2

⇒ z=1

∴ x=2, y=4, z=1 and t=3

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Chapter 5: Algebra of Matrices - Exercise 5.2 [Page 19]

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RD Sharma Mathematics [English] Class 12
Chapter 5 Algebra of Matrices
Exercise 5.2 | Q 19.1 | Page 19

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