NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 (Ex 4.1)
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‘Determinants’ is an essential chapter for students taking their Class 12 board exams. A determinant is calculated on a square matrix, and the obtained value is primarily a scalar quantity. The final value is to be computed based on particular properties and parameters of linear algebra.
Initially, it might seem confusing to students; however, with our Class 12 Maths Exercise 4.1 Solutions, you can avoid the mayhem. Consequently, you can also get deeper into the concept of determinants starting right from the basics. It will not only strengthen your fundamentals but also make ready for the twisted questions too.
Our solutions by Vedantu will help you to understand the topics clearly and then solve the numerical without any error. It will aid you in fetching higher grades in the exam too. Here is an overview of the exercise and the questions covered under it.
A 2x2 matrix is given in the first question, and you are asked to find the determinant of it. The elements present in the matrix are integers in this case; however, from our Class 12 Maths Exercise 4.1 Solutions, students will know that they need to consider that these elements could be anything – natural numbers, fractions, decimals or trigonometric identities, etc.
The method of finding the determinant although remains same in all the cases as mentioned above. However, students need to be careful with the process of solving these. Identifying the rows and columns is of utmost importance, and it is the first when delving into determinants.
Therefore, to know the process in a step by step manner, you can refer to our study material for Determinants and Matrices Exercise 4.1. Our standard study materials will guide you throughout the solution of this question and gaining an in-depth knowledge of the same.
The elements present in this 2x2 matrix are trigonometric identities and algebraic expressions. Students should be well versed with the process of evaluating the determinant to follow the same rule even here.
In our Class 12 Maths Exercise 4.1 Solutions, you will know how to replace the numbers with the provided elements irrespective of their type. However, basic trigonometric rules should also be kept in mind to find an absolute determinant.
The process involves simple expansion of the given matrix and similarly finding the value, as it is done in case of natural numbers. With regular practice, you can get a firm grasp on the chapter and also on the processes. It will help you avoid unnecessary confusion during the exam, and also gain an edge over others by scoring higher.
This question asks to prove the given equation. You should have prior understanding of multiplying a natural number with the matrix. On the other hand, understanding how to multiply a natural number to the obtained determinant is equally essential.
You should know that both of these are different from each other. However, both the resultants can be equal when a matrix is multiplied by different natural numbers. You can learn to find the results from our Exercise 4.1 Class 12 Maths NCERT solutions in the most natural way.
The best part of such questions is that you can check whether your answer is correct or not right from your solutions. If both the sides of that equation are same, then it is correct otherwise not.
Hence, after every calculation, make sure you equate both the sides and check whether they are equivalent or not. Keeping this small trick in mind will help you in gaining more marks too without worrying about committing any error.
Here, a 3x3 matrix is given, and you are asked to prove that multiplying its determinant with 27 is equal to multiplying the matrix with 3. A clear understanding of the previous question will help you in determining the approach to these questions.
Besides, you have to know how to multiply a natural number with a 3x3 matrix. Students often confuse between rows and columns while multiplying. To avoid such confusion, you can always refer to our PDF of Class 12 Maths Exercise 4.1 Solutions for clarity.
Our solutions will help you easily determine the elements while multiplying and also keep track of the element that you have already used in your calculations. As a result, you will commit lesser mistakes, and even improve your scores in exam significantly.
Under question 5, there are four matrices for which you need to calculate the determinants. All these are 3x3 matrices, and they are evaluated similarly as you evaluate for a 2x2 matrix.
However, there is a catch here; if you find a particular row to have more than one element as zero, then you can reduce the determinant equation to a single term. The other two terms get cancelled as they are multiplied by zero.
From our Class 12 Maths Chapter 4 Exercise 4.1 solutions, you can learn these tricks easily. We have explained the concept as well as have provided short tricks to help you memorise these rules effortlessly.
Question 6 involves a very straightforward approach as you are asked to determine the value of the determinant of this 3x3 matrix. You should be careful while expanding the rows for calculation. With every expansion, one of the elements in the first row gets omitted, and you have to consider the other elements.
Besides, make sure you are well acquainted with the process of determinant calculation to score high in your board exam. Also, you can cross-check with our Class 12 Maths Exercise 4.1 Solutions for strict evaluation of the answers that you have calculated.
It will give you an insight into the step by solutions of the same questions. Also, you may learn the simple tricks to calculate faster in the exam.
Here you have two matrices given in each question, where you need to find the value of ‘x’ from one of the matrices by equating them. To compare them, you need to frame the equation at first.
Be careful when dealing with x2 terms, as you are likely to obtain two values for the same. One of the values is negative, and the other is positive; therefore, you need to consider both the values while writing your final answer.
To get a stronghold on such calculations, you can avail our Class 12 Maths Exercise 4.1 Solutions and know how to use the rules of finding determinants.
It is the last question in exercise 4.1, and it is quite similar to the previous one. You are required to calculate the value of ‘x’ from the given two matrices which are given to be equal.
Hence, at first, you have to find the determinant of each matrix in terms of ‘x’ and thereafter equate them to solve for the value of ‘x’. Knowing it for the first time often seems a little complicated; however, with regular practice, you can gain a stronghold on the topic.
Here, you are provided with four options to select the answer out of them. The answer is in square root form, which shows that there are two values. However, do not get confused when you get such an answer, because a determinant can hold any value as an answer.
Simultaneously, you can also avail our Class 12 Maths Exercise 4.1 Solutions for an elaborate understanding. We have compiled the solutions to these questions in a compact way to guide you in solving them in the right way.
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