ML Aggarwal ISC Determinants Class-12 Maths APC Ch-4

ML Aggarwal ISC Determinants Class-12 Understanding APC Mathematics Solutions Chapter-4. Step by step Solutions of ML Aggarwal ISC Understanding APC Mathematics Class-12  Exercise 4.1, Exe 4.2 And Exe 4.3, Exe 4.4, Exe 4.5, Exe 4.6, Exe 4.7 With Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

ML Aggarwal ISC Determinants Class-12 Maths APC Ch-4

Class:	12th
Subject:	Mathematics
Chapter  :	Ch-4 Determinants Page-230, 330

Board	ISC
Writer	ML Aggarwal ISC Understanding Vol-I
Publications	APC Arya Publications

-: Select Topics :-

Exe-4.1, 

Exe-4.2, 

Exe-4.3, 

Exe-4.4,

Exe-4.5,

Exe-4.6,

Exe-4.7,

Chapter Test 

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ML Aggarwal ISC Determinants Class-12 Maths APC Ch-4

Determinant:

Determinant is the numerical value of the square matrix. So, to every square matrix A = [a_ij] of order n, we can associate a number (real or complex) called determinant of the square matrix A. It is denoted by det A or |A|.
Note
(i) Read |A| as determinant A not absolute value of A.
(ii) Determinant gives numerical value but matrix do not give numerical value.
(iii) A determinant always has an equal number of rows and columns, i.e. only square matrix have determinants.

Properties of Determinants

Let us now look on to the properties of the Determinants which is discussed in determinants for class 12:

• The value of the determinant remains unchanged if the rows and columns of a determinant are interchanged.
• If any two rows (or columns) of determinants are interchanged, then sign of determinants changes.
• If any two rows or columns of a determinant are equal or identical, then the value of the determinant is 0.
• If each element of a row or a column is multiplied by a constant value k, then the value of the determinant originally obtained is multiplied with k.
•  If some or all elements of a row or column of a determinant are expressed as a sum of two or more terms, then the determinant can be expressed as the sum of two or more determinants.
•  In the elements of any row or column of a determinant, if we add or subtract the multiples of corresponding elements of any other row or column, then the value of determinant remains unchanged.

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Exe-4.1, 

Page-230, 231

ML Aggarwal ISC Determinants Class-12 Maths APC Ch-4

Question 1:

Evaluate the following determinants :

(i)…………

…………….

Question 2:

Evaluate the following determinants :

(i)…………

…………….

Question 3:

(i) Find the value of ……… 27 degree.

(ii) Find the value of…………………………… 45 degree.

Question 4:

……………………

……………………

…………………..

Question 13:

Using cofactors of elements of second.

………………….

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Exe-4.2, 

Page-270, 271, 273, 274

ML Aggarwal Determinants Class-12 Maths APC Ch-4

Question 1:

Show that |A| = |B| Where ……………..

Question 2:

Without expanding , find the value of :

………………

Question 3:

…………………

………………..

………………….

Question 31:

In a triangle ABC, if ………… is an isosceles triangle.

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Exe-4.3, 

Page-276, 277

ML Aggarwal Determinants Class-12 Maths APC Ch-4

Question 1:

Using determinates, find the area of the triangle whose vertices are ;

(i) ………….

………….

Question 2:

Show that the point ……….. collinear.

Question 3:

…………………..

………………….

………………….

Question 9:

If the point ……… prove that a + b = ab.

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Exe-4.4, 

Page-294, 295, 296, 297

ML Aggarwal ISC Determinants Class-12 Maths APC Ch-4

Question 1:

(i) If the matrix ………… find x.

(ii) For what value …………… singular ?

(iii) If 0 < x ………….. value of x.

Question 2:

.,…………………….

……………………….

……………………..

Question 25:

(i) Find the matrix A satisfying the matrix equation

(ii) Find the matrix P satisfying the matrix equation.

………………

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Exe-4.5, 

Page-310, 311

ISC Determinants Class-12 Maths APC Ch-4

Question 1:

Use matrix method to solve …………… equation .

………………

Question 2:

Using matrix method, determine …………….. or inconsistent :

……………………

Question 3:

……………………

……………………

……………………

…………………….

Question 13:

Using matrix, solve the ………….. equation .

………………………..

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Exe-4.6, 

Page-319, 320,

ML Aggarwal Determinants Class-12 Maths APC Ch-4

Question 1:

Using Cramer’s rule ……………. linear equation .

……………………

Question 2:

……………………

……………………

……………………

Question 14:

If the equations x = cy …………….  + 2abc = 1.

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Exe-4.7, 

Page-328, 329, 330

ML Aggarwal ISC Class-12 Maths APC Ch-4

Question 1:

If |x| represents greatest integer less than …………………… of the determinant.

………………..

Question 2:

……………………

………………………

……………………..

Question 17:

Find the product of matrices.

………………………

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Chapter Test

Page-331, 332

ISC Determinants Class-12 Maths APC Ch-4

Question 1:

If A and B are square matrices of …………….. of |-5 AB|.

Question 2:

Using ……….. the following .

……………………

Question 3:

………………………

……………………..

………………………

Question 18:

Examine whether or not the system of equations

…………………….

-: End of Determinants ML Aggarwal Vol-I ISC Class-12 Solutions:-

Return to :- ML Aggarwal ISC Class-12 APC Understanding Maths Solutions

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