Q. 48 E4.0( 4 Votes )

Find the matrix A

Answer :


We know that the two matrices are eligible for their product only when the number of columns of first matrix is equal to the number of rows of the second matrix.


The matrix given on the RHS of the equation is a 3×3 matrix and the one given on the LHS of the equation is a 3×2 matrix.


Therefore, A has to be a 2×3 matrix.


Let,


So the given question becomes,



Now we will multiply the two matrices on LHS, we get



[as cij = ai1b1j + ai2b2j + … + ainbnj]



To satisfy the above equality condition, corresponding entries of the matrices should be equal, i.e.,


2a – d = – 1…(i),


2b – e = – 8….(ii),


2c – f = – 10…..(iii)


a = 1, b = – 2,c = – 5


– 3a + 4d = 9……..(iv),


– 3b + 4e = 22………(v),


– 3c + 4f = 15……..(vi)


Substitute the value of a in eqn(i), we get


2a – d = – 1 2(1) – d = – 1 d = 3


Substitute the value of b in eqn(ii), we get


2b – e = – 8 2( – 2) – e = – 8 – 4 – e = – 8 e = 4


Substitute the value of c in eqn(iii), we get


2c – f = – 10 2( – 5) – f = – 10 – 10 – f = – 10 f = 0


Now substituting these values in matrix A, we get


is the matrix A.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Using matrices, sMathematics - Board Papers

If possible, usinMathematics - Exemplar

If possible, usinMathematics - Exemplar

Using matrices, sMathematics - Board Papers

Prove that <span Mathematics - Board Papers

Find the value ofMathematics - Board Papers

If A is a <span lMathematics - Board Papers