two step equations math

In other words, a square matrix A is invertible if and only if A is a non-singular matrix. (c) If A and B are invertible square matrices, then (AB) - 1 = B - 1 A - 1 (d) If A and B are two non-singular square matrices of the same order, then AB and BA are also non-singular matr..

Solve the system of linear equations. x +2y + 3z = 6 2x + 4y + z = 7 3x + 2y + 9z = 14 using Cramer's rul..

Row Matrix - A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..

Question: How many words of different 4 letters can be formed out of 7 capital letters, 3 vowels and 8 consonants, if each word starts with a capital letter and contains at least one vowel? Answer: Any capital letter can be chosen as the first letter of each word. So there are 7 ways of..

This means that A + B = B + A, where A, B are 2 matrices of the same orde..

Question: A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry Part II, unless Part I is also borrowed. In how many ways can he choose the three books to be borrowed? Answer: There are two ways of selecting 3 ..

The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn different ways. The principle can ..

A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put d = 0 we get GP and if we put r = 1, we get an A..

In the above method note that To obtain D 1 , replace a 1 , a 2 , a 3 by d 1 , d 2 , d 3 in D To obtain D 2 , replace b 1 , b 2 , b 3 by d 1 , d 2 , d 3 in D To obtain D 3 , replace c 1 , c 2 , c 3 by d 1 , d 2 , d 3 in ..

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..