CBSE Class 12-science Answered

What are Augumented matrices? And how to solve them.explain by giving example

Asked by rakshitreshu1997 | 05 Sep, 2015, 05:49: PM

Expert Answer

A u g m e n t e d space m a t r i x space i s space m a t r i x space o b t a i n e d space b y space a p p e n d i n g space a space r o w space o r space c o l u m n space t o space t h e space o r i g i n a l space m a t r i x. W h e n space t h e space s a m e space e l e m e n t a r y space o p e r a t i o n s space a r e space g o i n g space t o space t a k e space p l a c e space f o r space b o t h space t h e space m a t r i c e s comma space t h e space c o n c e p t space o f space a u g m e n t a t i o n space i s space u s e d. S u p p o s e space o u r space a i m space i s space t o space c o m p u t e space t h e space i n v e r s e space o f space a space m a t r i x. C o n s i d e r space a n space e x a m p l e colon L e t space A equals open square brackets table row 3 cell negative 2 end cell row 1 3 end table close square brackets comma space X equals open square brackets table row x row y end table close square brackets space a n d space B equals open square brackets table row 14 row 1 end table close square brackets Q u e s t i o n space g i v e n space i s comma space s o l v e space t h e space e q u a t i o n comma space A X equals B P r e m u l t i p l y space b y space A to the power of negative 1 end exponent comma space w e space h a v e comma space A to the power of negative 1 end exponent A X equals space A to the power of negative 1 end exponent B rightwards double arrow I X equals space A to the power of negative 1 end exponent B rightwards double arrow X equals space A to the power of negative 1 end exponent B T h u s space w e space n e e d space t o space f i n d space t h e space i n v e r s e space o f space t h e space m a t r i x space A space a n d space m u l t i p l y space i t space w i t h space B space t o g e t space t h e space s o l u t i o n. L e t space u s space A u g m e n t space t h e space m a t r i x space B space w i t h space A open square brackets table row 3 cell negative 2 end cell vertical ellipsis 14 row 1 3 vertical ellipsis 1 end table close square brackets T h e r e space i s space a space o n e space i n space t h e space f i r s t space c o l u m n space b u t space i n space t h e space s e c o n d space r o w. space H e n c e space w e space n e e d space t o space i n t e r c h a n g e space t h e space t w o space r o w s. A p p l y i n g space R subscript 1 left right arrow R subscript 2 comma space w e space h a v e comma open square brackets table row 1 3 vertical ellipsis 1 row 3 cell negative 2 end cell vertical ellipsis 14 end table close square brackets T o space g e t space a space z e r o space i n space t h e space l o w e r space l e f t space h a n d space c o r n e r comma space w e space n e e d space t o space a d d space minus 3 space t i m e s space r o w space 1 space w i t h space r o w space 2. A p p l y i n g space R subscript 2 rightwards arrow R subscript 2 minus 3 R subscript 1 comma space w e space h a v e comma open square brackets table row 1 3 vertical ellipsis 1 row 0 cell negative 11 end cell vertical ellipsis 11 end table close square brackets T o space g e t space a space 1 space i n space t h e space l o w e r space r i g h t space h a n d space c o r n e r comma space w e space n e e d space t o space d i v i d e space r o w space 2 space b y space minus 11. A p p l y i n g space R subscript 2 rightwards arrow fraction numerator negative R subscript 2 over denominator 11 end fraction comma space w e space h a v e comma open square brackets table row 1 3 vertical ellipsis 1 row 0 1 vertical ellipsis cell negative 1 end cell end table close square brackets T o space g e t space a space 0 space i n space t h e space u p p e r space r i g h t space h a n d space c o r n e r comma space a d d space minus 3 space t i m e s space r o w space 2 space w i t h space r o w space 1. A p p l y i n g space R subscript 1 rightwards arrow R subscript 1 minus 3 R subscript 2 comma space w e space h a v e comma open square brackets table row 1 0 vertical ellipsis 4 row 0 1 vertical ellipsis cell negative 1 end cell end table close square brackets T h u s space t h e space s o l u t i o n space o f space t h e space m a t r i x space i s space x equals 4 space a n d space y equals negative 1.

Answered by Vimala Ramamurthy | 06 Sep, 2015, 09:01: AM

CBSE Class 12-science Answered

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CBSE Class 12-science Answered

Concept Videos

Introduction to Matrices

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Elementary operations

Matrix and its order

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