# If A = [3 5], B =

We have the matrices A and B, such that  We need to find matric C, such that AC = BC.

Let C be a non-zero matrix of order 2 × 1, such that But order of C can be 2 × 1, 2 × 2, 2 × 3, 2 × 4, …

[ In order to multiply two matrices, A and B, the number of columns in A must equal the number of rows in B. Thus, if A is an m x n matrix and B is an r x s matrix, n = r.

, number of columns in matrix A = number of rows in matrix C = 2]

Take AC. Multiply 1st row of matrix A by matching members of 1st column of matrix C, then sum them up.

(3, 5)(x, y) = (3 × x) + (5 × y)

(3, 5)(x, y) = 3x + 5y  Now, take BC. Multiply 1st row of matrix B by matching members of 1st column of matrix C, then sum them up.

(7, 3)(x, y) = (7 × x) + (3 × y)

(7, 3)(x, y) = 7x + 3y  And,

AC = BC

[3x + 5y] = [7x + 3y]

3x + 5y = 7x + 3y

7x – 3x = 5y – 3y

4x = 2y

y = 2x

Then, Since, C is of orders, 2 × 1, 2 × 2, 2 × 3, … In general, Where, k is any real number.

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