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: 土 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 |
A3| = 27, then find the value of α
Ans:
土√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 6
Ans:
a2
+ b2 + c2 + d2Question 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-1B ⇒ 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-1B

⇒ 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-1B 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
Question 24
If A =
, B =
and X be a matrix such that A = BX, then find X
Answer: 
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