Question

if A =[ 1 2 3 4 ] adj A = [ 4 a -3 b ]
then the values of a and b are,
a=-2, b= 1
C) a= 2, b=-1
B) a= 2, b = 4
D) a = 1, b = -2​

Answer 1

Answer:

(C)

PLZ MAKE ME BRAINLIST

Answer 2

Answer:

A) a=-2, b= 1

Step-by-step explanation:

Concept= Adjoint of Matrix

Given= Matrix and its adjoint

To find= The missing value in adjoint

Explanation=

We have been the question as, if A =[ 1 2 3 4 ] adj A = [ 4 a -3 b ]

then the values of a and b are?

so,

Given A is 2 x 2 matrix

A= 1    2

    3   4

adj A= 4     a

         -3     b

adj A means Adjoint of matrix A.    

Adjoint of a 2 x 2 matrix is as follows,

let us suppose a matrix X such that

X =  u      v

      w      x

So now adjoint of this 2 x 2 matrix X will be said as adj X which is

adj X = x     -v

          -w     u

Now we compare the two matrix X and adj X.

We see that the right diagonal elements are interchanged and in the left diagonal only the element are multiplied by -1

So comparing the Matrix A and adj A, in this matrix the property will satisfy.

according to that,

A= 1     2           adj A = 4      a

    3     4                      -3      b

So the left diagonals element interchange then the value of b=1 and since the row 1 column 2 element remains but multiplied with -1  therefore a= -2.

Therefore the value of a= -2 and b= 1.

This value is satisfied by option A) a= -2 , b= 1

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