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 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

### 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 = [aij] 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.

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 13:

Using cofactors of elements of second.

………………….

### 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 31:

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

### 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 9:

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

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 25:

(i) Find the matrix A satisfying the matrix equation

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

………………

### 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 13:

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

………………………..

Exe-4.6,

Page-319, 320,

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

#### Question 1:

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

……………………

……………………

……………………

……………………

#### Question 14:

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

### 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 17:

Find the product of matrices.

………………………

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 18:

Examine whether or not the system of equations

…………………….

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

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