Construct a 2 x 2 matrix whose elements aij are given by aij = i.j - Mathematics

Construct a 2 x 2 matrix whose elements a_ij are given by a_ij = i.j

Sum

It can be `[(1, 2),(2, 4)]`.

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Chapter 8: Matrices - Exercise 8.1

Chapter 8 Matrices
Exercise 8.1 | Q 3.2

Wherever possible, write the following as a single matrix.

`[(1, 2),(3, 4)] + [(-1, -2),(1, -7)]`

Evaluate:

`2[(-1 0)/(2 -3)] +[(3 3)/(5 0)]`

If P= (8,5),(7,2) find : P + P^t

If A = `|(1,3),(3,2)|` and B = `|(-2 , 3),(-4 , 1)|` find BA

Let A = `|(3 , 2),(0 ,5)|` and B = `|(1 ,0),(1 ,2)|` , find (i) (A + B)(A - B) (ii) A² - B² . Is (i) equal to (ii) ?

Find the inverse of the matrix `[ (1, 2, 3), (1, 1, 5), (2, 4, 7)]` by using the adjoint method.
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Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.

If A = `[(7,1), (2,5)]` and B = `[(1,2), (3,-1)]` then verify that |AB| = |A| |B|.

If A = `[(1,0,0),(2,1,0),(3,3,1)]` then find A^-1 by using elementary transformation .

`[(2 , 7, 8),(-1 , sqrt(2), 0)]`