Example:
Solve the system of linear equations. x +2y + 3z = 6 2x + 4y + z = 7 3x + 2y + 9z = 14 using Cramer's rul..
Matrices
Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 c..
Consider the arrangement In this arrangement, there are two rows and four columns. The number 3 lies in the 2 n d row and 4 t h column. Each number has a fixed position. Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 c..Note:
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 ..
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 ..Suggested answer:
The arrangement is as shown in the figure, the boy X will have B 2 , B 3 as neighbours. The girl Y will have G 2 , G 3 as neighbours. The two boys B 2 , B 3 can be arranged in two ways. The two girls G 2 , G 3 can be arranged in two ways. Hence, the to..
The arrangement is as shown in the figure, the boy X will have B 2 , B 3 as neighbours. The girl Y will have G 2 , G 3 as neighbours. The two boys B 2 , B 3 can be arranged in two ways. The two girls G 2 , G 3 can be arranged in two ways. Hence, the to..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..
Example:
are all zero matrices of orders 1 x 2, 2 x 1, 2 x 2 and 3 x 3 respectivel..
are all zero matrices of orders 1 x 2, 2 x 1, 2 x 2 and 3 x 3 respectivel..Question 8
Question: There are three different rings to be worn in 5 fingers with at most one in each finger. In how many ways can this be done? Answer: For the first ring, there are 4 options as one finger cannot have more than one ring. The remaining two fingers will have 3 and 2 optio..
Harmonic Mean (H.M.)
If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other two. Example: 1/3, 1/7, 1/11 are in H.P., then 1/7 is the middle term. Hence 1/7 is the harmonic mean between 1/3 and 1/1..
Question 10
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle, we requir..
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle, we requir..Example:
The matrices are identify matrices of order 2 and 3 respectivel..
The matrices are identify matrices of order 2 and 3 respectivel..See what our Users say :
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