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Holiday HW

The document outlines a holiday assignment for students at Kendriya Vidyalaya RWF Yelahanka, Bengaluru, consisting of various mathematical problems involving matrices, determinants, and systems of equations. It includes tasks such as constructing matrices, solving for variables, verifying properties of matrices, and applying the matrix method to a real-world scenario involving cash awards. Students are required to demonstrate their understanding of linear algebra concepts through these exercises.

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19 views2 pages

Holiday HW

The document outlines a holiday assignment for students at Kendriya Vidyalaya RWF Yelahanka, Bengaluru, consisting of various mathematical problems involving matrices, determinants, and systems of equations. It includes tasks such as constructing matrices, solving for variables, verifying properties of matrices, and applying the matrix method to a real-world scenario involving cash awards. Students are required to demonstrate their understanding of linear algebra concepts through these exercises.

Uploaded by

rajkumar34287
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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KENDRIYA VIDYALAYA RWF YELAHANKA, BENGALURU – 560064

HOLIDAY ASSIGNMENT

1. Construct a 3 x3 matrix A = ( a ij ) when a ij = 5i + 3 j ,if i¿ j

=7 , if i =j

= 4i – 3 j ,if i¿ j

( ) ( )( )
2
x x −2
2. Solve for x and y when 2 −3 =
y 2y −9

(5 1 )
3. If A = 2 3 , Verify that A2 −8 A + 13 I = O and hence find A3

( 0 1)
4. If A = −1 0 (3 7 )
and B = 5 2 , , verify that P = B AB’ is a skew symmetric matrix

5. Using determinants , find the value of x for which the three points

A ( x , 2 −¿2x ) B ( −x +1 ,2 x ¿∧C (−4−x , 6−2 x ) are collinear

( )
2 3 −1
6. If A = x+ 4 −1 2 is singular matrix , find the value of x
3 x +1 2 −1

7. Let A = 3 (2 −1
4), B = ( )
5 2
7 4 , and C =
2 5
( )
3 8 , find the matrix D such that

CD – AB =O

( )
1 1 1
8. If A = 1 0 2 , find A−1 . Using A−1 ,solve x+y+z=6 ,x+2z=7
3 1 1

3x + y + z = 12

[ ] [ ]
1 −2 0 7 2 −6
9. . If A = 2 1 3 and B = −2 1 −3 , find AB. Hence, solve the system of equations:
0 −2 1 −4 2 5
x – 2y = 10; 2x + y + 3z = 8 and –2y + z = 7.

10 . A school wants to award its students for the values of Honesty, Regularity and Hard
work with a total cash award of Rs.6, 000/–. Three times the award money for Hard work
added to that given for Honesty amounts to Rs.11, 000/–. The award money given for
Honesty and Hard work together is double the one given for Regularity. Represent the above
situation algebraically and find the award money for each value, using matrix method

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