A triangle has 3 sides. Use the table to find the number of sides 5 tr..
A triangle has 3 sides. Use the table to find the number of sides 5 triangles will have. Number of Triangles 1 2 3 4 5 Number of Sides..
Geometrical Representation of Complex Number
(x 1 + x 2 ) + i (y 1 + y 2 ), i.e., z 1 + z 2 . The absolute values of z 1 , z 2 and z 1 + z 2 are geometrically given by We know that the sum of any two sides of a triangle is greater than the third. Hence, in D ORP, we have with the equality holding only..
(x 1 + x 2 ) + i (y 1 + y 2 ), i.e., z 1 + z 2 . The absolute values of z 1 , z 2 and z 1 + z 2 are geometrically given by We know that the sum of any two sides of a triangle is greater than the third. Hence, in D ORP, we have with the equality holding only..Example:
Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 ..
Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 ..Some important results
Some important results - Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then..
Some important results - Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then..Matrices and Determinants
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing resp..
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing resp..Surd
is NOT a surd because and 3 is NOT an irrational number. Without using tables, simplify: (i) 36 - 1 / 2 (ii) (i) 36 - 1 / 2 = (6 2 ) - 1 / 2 = 6 - 1 (i..
is NOT a surd because and 3 is NOT an irrational number. Without using tables, simplify: (i) 36 - 1 / 2 (ii) (i) 36 - 1 / 2 = (6 2 ) - 1 / 2 = 6 - 1 (i..Application of Determinants
Now we shall discuss the use of determinants in finding the area of a triangle and in the solution of simultaneous equation..
Conclusion
We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan method e..
Question 6
Question: Using the given values of a and d find the first five terms of A.P. and the general term. a = 4, d = 3 Answer: The first five terms are: ..
Question: Using the given values of a and d find the first five terms of A.P. and the general term. a = 4, d = 3 Answer: The first five terms are: ..Proof:
From the definition of inverse of a matrix, we have (AB)(AB) - 1 = I or A - 1 (AB)(AB) - 1 = A - 1 I (Pre-multiplying both sides by A - 1 ) or (A - 1 A) B (AB) - 1 = A - 1 (Since A - 1 I = A - 1 ) or I B (AB) - 1 = A - 1 or B (AB) - 1 = A - 1 or (B - 1..
Result
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