Home
Class 12
MATHS
Find the value of a if [a-b2a+c2a-b3c+d]...

Find the value of `a` if `[a-b2a+c2a-b3c+d]=[-1 5 0 13]`

Text Solution

Verified by Experts

The correct Answer is:
`a=1, b=2, c=3, d=4`
`[(a-b,2a+c),(2a-b,3c+d)]=[(-1,5),(0,13)]`
As the two matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get
`a-b=-1` (1)
`2a-b=0` (2)
`2a+c=5` (3)
`3c+d=13` (4)
From (2), we have
`b=2a`
Then, from (1), we have
`a-2a=-1`
or `a=1`
`implies b=2`
Now, from (3), we have
`2xx1+c=5`
or `c=3`
From (4), we have
`3xx3+d=13`
or `9+d=13` or `d=4`
`:. a=1, b=2, c=3` and `d=4`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise 13.2|6 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.3|10 Videos

  • MATRICES

    CENGAGE|Exercise Examples|75 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

Write each of the following in the form of ax + by + c = 0 and find the values of a, b and c (i) 2x = 5 (ii) y - 2 = 0 (iii) y/7=3 (iv) x= (-14)/13

Find the value of lambda if the points A(-1, 4, -3) B(3, lambda , - 5), C (-3 ,8,-5) D(-3, 2, 1) are coplanar.

Find the value of a, b, c, d from the equation ((a-b,2a+c),(2a-b,3c+d))=((1,5),(0,2))

Find the value of a , b , c , d , x , y from the following matrix equation . ({:(d , 8) , (3b , a):}) + ({:(3 , a) , (-2 , -4):})= ({:(2 , 2a) , (b , 4c):}) + ({:(0 , 1) , (-5 , 0):})

If A=[0 1 2 1 2 3 3a1]a n d A_1=[1//2 12//12//-4 3c5//2-3//2 1//2] , then the values of a anti c are equal to 1,1 b. 1,-1 c. 1,2 d. -1,1

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the minimum value of a+b+c is (a) 1 (b) 3 (c) 5 (d) 9

Let A B C be a triangle. Let A be the point (1,2),y=x be the perpendicular bisector of A B , and x-2y+1=0 be the angle bisector of /_C . If the equation of B C is given by a x+b y-5=0 , then the value of a+b is (a) 1 (b) 2 (c) 3 (d) 4