NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.6

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.6 is given in this article with a detailed explanation. Chapter 4 Determinants Exercise 4.6 covers concepts of applications of determinants and matrices and finding the solution of a given system of linear equations using an inverse of a matrix.

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Class 12 Maths Chapter 4 Determinants Topics:

Determinants and Matrices	Elementary Matrix Operations	Difference between rows and columns
Properties of Determinants	Inverse Laplace Transform	Consistent System of Linear Equations
Jacobian Method	Minors and Cofactors	Non-singular matrix

CBSE Class 12 Maths Study Guides:

Math MCQs	Math Study Notes	Math Formula
Algebra	Difference between in Maths	NCERT Solutions for Class 12 Maths
Calculus	Probability and Statistics	Arithmetic
Mensuration	Trigonometry	Geometry

CBSE CLASS XII Related Questions

1.
Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

View Solution

2.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

View Solution

3.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

View Solution

4.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

View Solution

5.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

View Solution

6.
If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

\(x^4+\frac{1}{x^3}-\frac{129}{8}\)
\(x^3+\frac{1}{x^4}+\frac{129}{8}\)
\(x^4+\frac{1}{x^3}+\frac{129}{8}\)
\(x^3+\frac{1}{x^4}-\frac{129}{8}\)

View Solution

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CBSE CLASS XII Previous Year Papers

Mathematics

Mathematics Preparation Guides

Matrices: Types, Properties, Formulas & Examples

Relations and Functions: Explanation, Types, and Representation

Types of Matrices: Row, Column, Zero, Symmetric, Skew Symmetric

Minors and Cofactors of Determinant: Definition, Formula and Solved Examples

Operations on Matrices: Addition, Subtraction, Multiplication and Solved Examples

Determinants: Types, Properties & Examples

Types of Relations: Definition, Classification and Examples

Properties of Determinants: Explanation, Important Properties and Examples

Plane: Equation of a Plane in Three-Dimensional Space

Invertible Matrices: Theorems, Properties and Examples

Symmetric and Skew Symmetric Matrices: Definition and Properties

Types of Functions: Elements, Equations, Range, and Domain

Introduction to Three-Dimensional Geometry: Distance, Important Formulae

Angle between Two Lines: Formula, Derivation & Calculation

Binary Operations: Types, Properties and Examples

Addition of Vectors: Definition, Formula, Laws and Properties

Types of Vectors: Definition, Properties & Examples

Definite Integral: Formula, Properties, Application & Examples

Integration by Partial Fractions: Formula, Steps & Examples

Angle Between a Line and a Plane: Formulas and Solved Examples

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.6

CBSE CLASS XII Related Questions

1.
Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

2.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

3.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

4.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

5.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

6.
If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.6

CBSE CLASS XII Related Questions

1. Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

2. Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

3. If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that (i) \((A+B)'=A'+B' \)(ii) \((A-B)'=A'-B'\)

4. Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)n=anI+nan-1bA,where I is the identity matrix of order 2 and n∈N

5. If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

6. If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)

2.
Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)

3.
If A'= \(\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 &1 \end{bmatrix}\)\(\begin{bmatrix} -1 & 2 & 1 \\ 1 &2 & 3\end{bmatrix}\) , then verify that
(i) \((A+B)'=A'+B' \)
(ii) \((A-B)'=A'-B'\)

4.
Let A=\(\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}\),show that(aI+bA)ⁿ=aⁿI+na^n-1bA,where I is the identity matrix of order 2 and n∈N

5.
If (i) A=\(\begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha \end{bmatrix}\),then verify that A'A=I
(ii) A= \(\begin{bmatrix} \sin\alpha & \cos\alpha\\ -\cos \alpha & \sin\alpha \end{bmatrix}\),then verify that A'A=I

6.
If \(\frac{d}{dx}f(x) = 4x^3-\frac{3}{x^4}\) such that \(f(2)=0\), then \(f(x)\) is