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Matrices

Long Answer Type

141. You are given the net-work of air routes between the airports of three countries X, Y and Z.

Find the net-work matrices connecting the countries:
(i) X to Y (ii) Y to Z

95 Views

Short Answer Type

142.

If space straight f left parenthesis straight x right parenthesis space equals space straight x squared minus 5 straight x plus 7 space. space Find space straight f left parenthesis straight A right parenthesis space where space straight A equals space open square brackets table row 3 1 row cell negative 1 end cell 2 end table close square brackets

72 Views

143.

Find space straight f left parenthesis straight A right parenthesis space comma space given space straight f left parenthesis straight X right parenthesis space equals space straight x squared minus 7 straight x minus 2 space and space straight A equals space open square brackets table row cell 2 space space end cell 3 row 4 5 end table close square brackets

72 Views

Long Answer Type

144.

Let space straight A equals space open square brackets table row 2 cell space 3 end cell row cell negative 1 end cell cell space 2 end cell end table close square brackets space and space straight f space left parenthesis straight x right parenthesis space equals space straight x squared minus 4 straight x plus 7 space show space that space straight f left parenthesis straight A right parenthesis space equals space straight O. space use space this space result space to space find space straight A to the power of 5

76 Views

145. $If space straight A equals space open square brackets table row cell 1 space space end cell cell space space space 0 end cell cell space space space 2 end cell row 0 cell space space 2 end cell cell space space space 1 end cell row 2 cell space 0 end cell cell space 3 end cell end table close square brackets space then space show space that space straight A cubed space minus 6 straight A squared space plus 7 straight A space plus space 2 space straight I equals space straight O$

H e r e space space straight A equals space open square brackets table row cell 1 space end cell 0 cell space space 2 end cell row cell 0 space space end cell 2 cell space 1 end cell row 2 cell space 0 end cell cell space 3 end cell end table close square brackets straight A squared space equals open square brackets table row cell 1 space end cell 0 cell space space 2 end cell row cell 0 space space end cell 2 cell space 1 end cell row 2 cell space 0 end cell cell space 3 end cell end table close square brackets space space open square brackets table row cell 1 space end cell 0 cell space space 2 end cell row cell 0 space space end cell 2 cell space 1 end cell row 2 cell space 0 end cell cell space 3 end cell end table close square brackets space space space space space space equals space space open square brackets table row cell 1 plus 0 plus 4 space space space end cell cell space space 0 plus 0 plus 0 end cell cell space space space 2 plus 0 plus 6 end cell row cell 0 plus 0 plus 2 end cell cell space space 0 plus 4 plus 0 end cell cell space space space 0 plus 2 plus 3 end cell row cell 2 plus 0 plus 6 end cell cell space space 0 plus 0 plus 0 end cell cell space space 4 plus 0 plus 9 end cell end table close square brackets space space equals space open square brackets table row 5 cell space space space space 0 end cell cell space space 8 end cell row 2 cell space space space 4 end cell cell space space 5 end cell row 8 cell space space space 0 end cell cell space space 13 end cell end table close square brackets straight A cubed space equals space space open square brackets table row cell 5 space space space end cell cell space space space 0 end cell cell space space space 8 end cell row 2 cell space space 4 end cell cell space space 5 end cell row 8 cell space space 0 end cell cell space space space 13 end cell end table close square brackets space space open square brackets table row 1 cell space space space space 0 end cell cell space space space 2 end cell row 0 cell space space space space 2 end cell cell space space 1 end cell row 2 cell space space space 0 end cell cell space space 3 end cell end table close square brackets space space space space space equals space space open square brackets table row cell 5 plus 0 plus 16 end cell cell space space space space 0 plus 0 plus 0 end cell cell space space space 10 plus 0 plus 24 end cell row cell 2 plus 0 plus 16 end cell cell space space space space 0 plus 8 plus 0 end cell cell space space 4 plus 4 plus 15 end cell row cell 8 plus 0 plus 26 end cell cell space space space space 0 plus 0 plus 0 end cell cell space space 16 plus 0 plus 39 end cell end table close square brackets space equals space open square brackets table row cell 21 space space end cell 0 cell space space 34 end cell row cell 12 space space end cell 8 cell space space 23 end cell row 34 0 cell space space 55 end cell end table close square brackets C o n s i d e r space straight A cubed space minus 6 straight A plus 7 straight A plus 21 space space space space space equals space open square brackets table row cell 21 space space end cell 0 cell space space 34 end cell row cell 12 space space end cell 8 cell space space 23 end cell row 34 0 cell space space 55 end cell end table close square brackets minus 6 space space open square brackets table row 5 cell space space space space 0 end cell cell space space space 8 end cell row 2 cell space space space space 4 end cell cell space space space 5 end cell row 8 cell space space space space 0 end cell cell space space space 13 end cell end table close square brackets plus 7 space open square brackets table row 1 cell space space space space space 0 end cell cell space space space 2 end cell row 0 cell space space space space space 2 end cell cell space space 1 end cell row 2 cell space space space space 0 end cell cell space space 3 end cell end table close square brackets plus 2 space open square brackets table row 1 cell space space space space 0 end cell cell space space space 0 end cell row 0 cell space space space 1 end cell cell space space space 0 end cell row 0 cell space space space 0 end cell cell space space space 1 end cell end table close square brackets space space space space equals space space open square brackets table row cell 21 space space end cell 0 cell space space 34 end cell row cell 12 space space end cell 8 cell space space 23 end cell row 34 0 cell space space 55 end cell end table close square brackets space plus space open square brackets table row cell negative 30 end cell cell space space space 0 end cell cell space space minus 48 end cell row cell negative 12 space space space end cell cell negative 24 end cell cell space space minus 30 end cell row cell negative 48 end cell cell space space 0 end cell cell space minus 78 end cell end table close square brackets plus space open square brackets table row 7 cell space space space 0 end cell cell space space space 14 end cell row 0 cell space space space 14 end cell cell space space space 7 end cell row 14 cell space space space 0 end cell cell space space space 21 end cell end table close square brackets plus space open square brackets table row 2 cell space space space 0 end cell cell space space space 0 end cell row 0 cell space space space 2 end cell cell space space 0 end cell row cell 0 space end cell cell space space space 0 end cell cell space space 2 end cell end table close square brackets space space space equals space space open square brackets table row cell 21 minus 30 plus 7 plus 2 end cell cell space space space space space space space space space space space space space space space space 0 plus 0 plus 0 plus 0 end cell cell space space space space space space space space space 34 minus 48 plus 14 plus 0 end cell row cell 12 minus 12 plus 0 plus 0 end cell cell space space space space space space space space space space 8 minus 24 plus 14 plus 2 end cell cell space space space space space space space space space space space 23 minus 30 plus 7 plus 0 end cell row cell 34 minus 48 plus 14 plus 0 end cell cell space space space space space space space space space space space space space space space space space space space space space 0 plus 0 plus 0 plus 0 end cell cell space space space space space space space space space space space 55 minus 78 plus 21 plus 2 end cell end table close square brackets space space space space equals space space open square brackets table row 0 cell space space space 0 end cell cell space space space 0 end cell row 0 cell space space space 0 end cell cell space space space space 0 end cell row 0 cell space space space 0 end cell cell space space space 0 end cell end table close square brackets equals space straight O therefore space space straight A cubed space minus 6 straight A squared plus 7 straight A plus 2 space straight I space equals space straight O

75 Views

146.

If space straight A equals space open square brackets table row 1 2 3 row 3 cell negative 2 end cell 1 row 4 2 1 end table close square brackets space comma space then space straight A cubed space minus 23 space straight A space 40 space straight I space equals straight O

85 Views

Short Answer Type

147. A matrix X has a + b rows and a + 2 columns while the matrix Y has b + 1 rows and a + 3 columns. Both matrices XY and YX exist. Find a and b. Can you say that XY and YX are of the same type. Are they equal ?

205 Views

Long Answer Type

148.

Given space straight A equals space open square brackets table row 1 cell space space minus 1 end cell cell space space 1 end cell row cell 1 space space end cell cell space space space space minus 2 space space end cell cell negative 2 end cell row 2 cell space space space space space 1 end cell cell space space 3 end cell end table close square brackets space comma space straight B equals space open square brackets table row cell negative 4 end cell cell space space space 4 end cell cell space space space 4 end cell row cell negative 7 end cell cell space space space 1 end cell cell space space space space 3 end cell row 5 cell space space space space space minus 3 space space space space end cell cell negative 1 end cell end table close square brackets space find space AB space and space use space this space result space in space solving space the space following space system space of space equations space colon space space straight x space – space straight y space plus space straight z space equals space 4 space „ straight y space – space 2 straight y space – space 2 straight z space equals space 9 comma space 2 straight X space plus space straight Y space plus space 3 straight z space equals space 1. space

88 Views

149.

use space product space space open square brackets table row 1 cell negative 1 end cell cell space space space 2 end cell row 0 cell space space space 2 end cell cell space space minus 3 end cell row 3 cell negative 2 end cell cell space space space space 4 end cell end table close square brackets space space open square brackets table row cell negative 2 end cell cell space space space 0 end cell cell space space 1 end cell row 9 cell space space space 2 end cell cell space space space minus 3 end cell row 6 cell space space space 1 end cell cell space space space minus 2 end cell end table close square brackets space to space solve space the space system space of space equations

81 Views

150.

Syntax error from line 1 column 1300 to line 1 column 1307.

85 Views