Best Study Notes » Mathematics XII
Maths - Class XII - CBSE Sample paper - Set 2 Part A
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Maths - Class XII - CBSE Sample paper
Determination of Square Matrix of order 2
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Free Coaching Classes XII - Maths - Algebra - Matrices
Multiplication of Matrices - Numerical Example
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Free Coaching Class for XII - Maths - Algebra - Matrices
Adjoint of a Matrix
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The Adjoint of a matrix is the matrix formed by taking the transpose of the cofactor matrix of a given original matrix. Here are steps to find it out:
1. Original Matrix A
2. Cofactor of Matrix A
3. Transpose the Cofactor
4. Result is the Adjoint matrix
1. Original Matrix A
2. Cofactor of Matrix A
3. Transpose the Cofactor
4. Result is the Adjoint matrix
How to find determinants of a 3x3 matrix
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A determinant can be expanded along any of its row (or column). For
easier calculations it must be expanded along the row (or column)
containing maximum zeros. Value of determinant of a matrix A is obtained by sum of product of
elements of a row (or a column) with corresponding cofactors. For
example |A|= a11A11+a12A12+a13A13. If elements of a row (or column) are multiplied with cofactors of
easier calculations it must be expanded along the row (or column)
containing maximum zeros. Value of determinant of a matrix A is obtained by sum of product of
elements of a row (or a column) with corresponding cofactors. For
example |A|= a11A11+a12A12+a13A13. If elements of a row (or column) are multiplied with cofactors of
Types of Matrices
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Order of a matrix gives the number of rows and columns present in the
matrix. The simplest classification of matrices is based on the order of the matrix. Two matrices can be added9or subtracted) if they are of same order. For
multiplying two matrices A and B number of columns in A must be equal to
the number of rows in B.
matrix. The simplest classification of matrices is based on the order of the matrix. Two matrices can be added9or subtracted) if they are of same order. For
multiplying two matrices A and B number of columns in A must be equal to
the number of rows in B.
Inverse Trigonometric functions - graphs - 2
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The inverse trigonometric functions are the inverse functions of the trigonometric functions. The value of an inverse trigonometric function which lies in the range
of principal branch is called the principal value of the inverse
trigonometric functions.Inverse of a function is not equal to the reciprocal of the function
of principal branch is called the principal value of the inverse
trigonometric functions.Inverse of a function is not equal to the reciprocal of the function
Inverse Trigonometric functions - graphs
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Inverse trigonometric functions map real numbers back to angles. The graph of sin^-1 x can be obtained from the graph of sine x by interchanging the x and y axes. Graph of the inverse function is the mirror image (i.e. reflection) of the
original function along the line y = x.
original function along the line y = x.
Inverse Functions
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A function f : X -> Y is defined to be invertible, if there exists a function
g : Y -> X such that gof = IX and fog = IY. The function g is called the inverse of f and is denoted by f ^–1. Thus, the inverse of a function is a function that looks at this relationship from the other viewpoint.
g : Y -> X such that gof = IX and fog = IY. The function g is called the inverse of f and is denoted by f ^–1. Thus, the inverse of a function is a function that looks at this relationship from the other viewpoint.
Composition of Functions - 2
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The term "composition of functions" (or "composite function") refers to the combining of functions in a manner where the output from one function becomes the input for the other function.
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xii - maths - algebra - determinants
xii - maths - algebra - matrices
xii - maths - relations and functions