Here you will learn formula for finding the equation of directrix of parabola with examples. Let’s begin – Equation of Directrix of Parabola (i) For Parabola \(y^2\) = 4ax : The equation of directrix is x = -a. (ii) For Parabola \(y^2\) = -4ax : The equation of directrix is x = a. (iii) For […]
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Here you will learn formula to find the length of latus rectum of parabola with examples. Let’s begin – Latus Rectum of Parabola A double ordinate through the focus is called the latus rectum i.e. the latus rectum of a parabola is a chord passing through the focus perpendicular to the axis. In the given
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Here you will learn what is integration by substitution method class 12 with examples. Let’s begin – Integration By Substitution The method of evaluating an integral by reducing it to standard form by a proper substitution is called integration by substitution. If \(\phi(x)\) is continuously differentiable function, then to evaluate integrals of the form \(\int\)
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Here you will learn what is singular matrix definition with examples and also determinant of singular matrix. Let’s begin – Singular Matrix Definition : A square matrix is a singular matrix if its determinant is zero. Otherwise, it is a non-singular matrix. Also Read : How to Find the Determinant of Matrix Example : Show
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Here you will learn what is the matrix polynomial definition with examples. Let’s begin – Matrix Polynomial Definition : Let f(x) = \(a_0x^n\) + \(a_1x^{n – 1}\) + \(a_2x^{n – 2}\) + ……. + \(a_{n – 1}x\) + \(a_n\) be a polynomial and let A be a square matrix of order n. Then, f(A) =
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Here you will learn what is the lower triangular matrix definition with examples. Let’s begin – Lower Triangular Matrix Definition : A square matrix A = \([a_{ij}]\) is called an lower triangular matrix if \(a_{ij}\) = 0 for all i < j. Thus, in an lower triangular matrix, all elements above the main diagonal are
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Here you will learn what is the upper triangular matrix definition with examples. Let’s begin – Upper Triangular Matrix Definition : A square matrix A = \([a_{ij}]\) is called an upper triangular matrix if \(a_{ij}\) = 0 for all i > j. Thus, in an upper triangular matrix, all elements below the main diagonal are
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Here you will learn what is the zero or null matrix definition with examples. Let’s begin – Zero or Null Matrix Definition : A matrix in which al elements are zero is called a null or a zero matrix. Also Read : Different Types of Matrices – Definitions and Examples Examples : 1). \(\begin{bmatrix} 0
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Here you will learn what is the identity or unit matrix definition with examples. Let’s begin – Identity or Unit Matrix Definition : A square matrix A = \([a_{ij}]_{n\times n}\) is called a identity or unit matrix if (i) \(a_{ij}\) = 0 for all i \(\ne\) j and, (ii) \(a_{ii}\) = 1, for all i
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Here you will learn what is the scalar matrix definition and order of scalar matrix with examples. Let’s begin – Scalar Matrix Definition : A square matrix A = \([a_{ij}]_{n\times n}\) is called a scalar matrix if (i) \(a_{ij}\) = 0 for all i \(\ne\) j and, (ii) \(a_{ii}\) = c, for all i, where
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