## Math Assignment Class XII Ch - 04

**DETERMINANTS**

**Extra questions of chapter 04 Determinants class XII with answers and hints to the difficult questions, strictly according to the CBSE syllabus. Important and useful math. assignment for the students of class XII**

**MATHEMATICS ASSIGNMENT ON **

**DETERMINANTS (XII)**

**Strictly according to the CBSE Board**

Question 1

Find the value of k for which matrix A is a singular matrix

Ans: åœŸ 4

Question 2

If A is a square matrix of order 3 and |A| = -4, then find the value of |adj A|

Ans: 16

Question 3

,

and |

A^{3}| = 27, then find the value of Î±

Ans:

åœŸ√7

Question 4

, then find the value of x

Ans : x = 9

Question 5 then verify that |AB| = |A||B|

Solution Hint: |AB| = 77 and |A||B| = 7 x 11 = 77

Question 6Ans:

a^{2}
+ b^{2} + c^{2} + d^{2}Question 7

Ans: 0

Question 8

For what value of x, the matrix A is singular

Question 9

Find the area of triangle with vertices A(5, 4), B(-2, 4), C(2, -6)

Ans: 35 sq unit

Question 10

Using determinants show that the points (2, 3), (-1, -2) and (5, 8) are collinear

Solution Hint:

Find area of triangle by taking above given points as vertices.

If area of triangle = 0 then points are collinear.

Question 11

Using determinants find the value of k so that the points (k, 2 - 2k), (- k + 1, 2k), and (- 4 - k, 6 - 2k) may be collinear

Ans: k = -1, 1/2

Question 12Using determinants, find the equation of line joining the points (3,1), and (9,3)

Ans: x - 3y = 0

Question 13

Find the value of k, if area of triangle is 4 square units whose vertices are (-2,0), (0,4), and (0, k)

Ans: K = 0, 8

Question 14

Find the value of |AB| if matrices A and B are given below

and

Ans: 0

Question 15

Find the value of x if matrix A is a singular matrix

Ans: x = -4

Question 16

Find the product :

Hence solve the following system of equations

x - y = 3, 2x + 3y + 4z = 17, y + 2z = 7

Ans: x = 2, y = -1, z = 4

Solution Hint

Let given matrices are A and C

Now find the product AC we get

Now given system of equations can be written as

AX = B ⇒ X = A^{-1}B ⇒ x = 2, y = -1, z = 4 is the required solution

Question 17

Find

A^{-1 }and hence solve following system of equations

3x - 4y + 2z = -1, 2x + 3y + 5z = 7, x + z = 2

Ans: x = 3, y = 2, z = -1

Solution Hint:

Find |A| we find |A| = -9 ⇒ A is invertible

Find cofactors of A and then find Adj. A we get

Find A^{-1 }we get

Given system of equations can be written as AX = B

⇒ X= A^{-1}B

⇒ x = 3, y = 2, z = -1Question 18

Find

A^{-1}. Use A-1 to solve the system of equations.

2x – 3y + 5z = 11, 3x + 2y – 4z = - 5, x + y - 2z = - 3

Ans: x = 1, y = 2, z = 3

Solution Hint

Find the |A| we get |A| = -1

Find adjoint of A

Solve: X = A^{-1}B we get x = 1, y = 2, z = 3

Question 19

Show that the matrix A satisfies the equation A

^{2 } - 4A - 5I = O and hence find

A^{-1}Ans:

Question 20

Find the matrix X for which

Ans

Question 21

Ans:

Question 22

Solve the following system of equations

x + y + z = 3, 2x - y + z = -1, 2x + y - 3z = -9

Ans: x = -8/7, y=10/7, z=19/7

Question 23

Solve the following system of equations

where x, y, z ≠ 0

Ans: x = 2, y = 3, z = 5

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