Matrices and Determinants Summary
The system of linear equations may be expressed as AX = B. Step 2: Find |A|. If |A| 0, the system has unique solution which is given by X = A - 1 B. Step 3: If |A| = 0, put x = k (y = k or z = k) in any two of the given equations and find ..
The system of linear equations may be expressed as AX = B. Step 2: Find |A|. If |A| 0, the system has unique solution which is given by X = A - 1 B. Step 3: If |A| = 0, put x = k (y = k or z = k) in any two of the given equations and find ..Multiplication of Matrices
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can b..
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can b..To insert n Harmonic Means between two given quantities
Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h 2..
Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h 2..To find the harmonic mean between two given quantities
Let H be the harmonic mean between the quantities a and b. ..
Let H be the harmonic mean between the quantities a and b. ..Question 2
Question: A lady wants to select one cotton saree and one polyster saree from a collection of 8 cotton sarees and 11 polyster sarees. In how many ways can the lady choose the two sarees? Answer: Here, there are two events E 1 and E 2 . E 1 = Selection of ..
Question: A lady wants to select one cotton saree and one polyster saree from a collection of 8 cotton sarees and 11 polyster sarees. In how many ways can the lady choose the two sarees? Answer: Here, there are two events E 1 and E 2 . E 1 = Selection of ..Question 2
Question: vi) (n! + 1) is not divisible by any natural number between 2 and n. vii) Simplify Answer: ..
Question: vi) (n! + 1) is not divisible by any natural number between 2 and n. vii) Simplify Answer: ..Question 2
Question: Answer: i. The value of C(n, 25) = C(25, 25) = 1 ii..
Question: Answer: i. The value of C(n, 25) = C(25, 25) = 1 ii..Corollary 2:
C(n,0) = C(n,n) =..
Cramer's rule for the solution of a system of equations in 2 variables
We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..
We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio.. Result
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