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

Here space straight f left parenthesis straight x right parenthesis equals straight x squared minus 7 straight x minus 2 therefore space space space space space straight f left parenthesis straight A right parenthesis space equals straight A squared space space minus 7 straight A minus 2 space straight I space space space space space space space space space space space straight A space equals space open square brackets table row 2 cell space space 3 end cell row 4 cell space space 5 end cell end table close square brackets space space space space space space space space space space space space straight A squared space equals space open square brackets table row 2 cell space space 3 end cell row 4 cell space space 5 end cell end table close square brackets space space open square brackets table row 2 cell space space 3 end cell row 4 cell space space 5 end cell end table close square brackets space equals space open square brackets table row cell 4 plus 12 end cell cell space space 6 plus 15 end cell row cell 8 plus 20 end cell cell space space 12 plus 25 end cell end table close square brackets space space space equals space open square brackets table row 16 cell space 21 end cell row 28 cell space 37 end cell end table close square brackets space space space space space space space space straight f left parenthesis straight A right parenthesis space equals straight A squared space space minus 7 straight A minus 2 space straight I space space space space space space space space space space space space space space space space equals space open square brackets table row 16 cell space space 21 end cell row 28 cell space space 37 end cell end table close square brackets space minus 7 space open square brackets table row bold 2 cell bold space bold space bold 3 end cell row bold 4 cell bold space bold space bold 5 end cell end table close square brackets minus 2 space open square brackets table row bold 1 cell bold space bold 0 end cell row bold 0 cell bold space bold space bold 1 end cell end table close square brackets space space space space space space space space space space space space space space space space equals space open square brackets table row 16 cell space space 21 end cell row 28 cell space space 37 end cell end table close square brackets plus open square brackets table row cell negative 14 end cell cell negative 21 end cell row cell negative 28 end cell cell negative 35 end cell end table close square brackets plus space open square brackets table row cell negative 2 end cell cell bold space bold 0 end cell row bold 0 cell bold space bold space bold minus bold 2 end cell end table close square brackets space space space space space space space space space space space space space space space equals space open square brackets table row cell 16 minus 14 minus 2 end cell cell space space 21 minus 21 plus 0 end cell row cell 28 minus 28 plus 0 space end cell cell space space 37 minus 35 minus 2 end cell end table close square brackets equals space open square brackets table row 0 cell space space 0 end cell row 0 cell space space 0 end cell end table close square brackets therefore space space space space space space space space space space space straight f left parenthesis straight A right parenthesis equals straight O

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

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