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

we space have space comma space straight f left parenthesis straight x right parenthesis equals straight x squared minus 4 straight x plus 7 therefore space space straight f space left parenthesis straight A right parenthesis equals space straight A squared space minus 4 straight A space plus space 7 space straight I subscript 2 space Now space space space straight A equals space open square brackets table row 2 cell space space 3 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space space space space space space space space space space space straight A squared space space equals space open square brackets table row 2 cell space space 3 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space space open square brackets table row 2 cell space space 3 end cell row cell negative 1 end cell cell space space 2 end cell end table close square brackets space space space space space equals space space open square brackets table row cell 4 minus 3 end cell cell space space space space space space space 6 plus 6 end cell row cell negative 2 minus 2 end cell cell space space minus 3 plus 4 end cell end table close square brackets equals space open square brackets table row 1 cell space space 12 end cell row cell negative 4 end cell cell space space 1 end cell end table close square brackets space space space space space space space space minus 4 straight A space equals space open square brackets table row cell negative 8 end cell cell space space minus 12 end cell row 4 cell space minus 8 end cell end table close square brackets space and space 7 space straight I subscript 2 space equals space open square brackets table row 7 cell space space 0 end cell row 0 cell space space 7 end cell end table close square brackets therefore space space space space straight f space left parenthesis straight A right parenthesis space equals space straight A squared minus 4 straight A plus 7 space straight I subscript 2 rightwards double arrow space space space space straight f space left parenthesis straight A right parenthesis space equals space open square brackets table row 1 cell space space 12 end cell row cell negative 4 end cell cell space 1 end cell end table close square brackets plus space open square brackets table row cell negative 8 end cell cell space space minus 12 end cell row 4 cell space minus 8 end cell end table close square brackets space plus space open square brackets table row 7 cell space space 0 end cell row 0 cell space space 7 end cell end table close square brackets rightwards double arrow space space space space straight f space left parenthesis straight A right parenthesis space equals space open square brackets table row cell 1 minus 8 plus 7 end cell cell 12 minus 12 plus 0 end cell row cell negative 4 plus 4 plus 0 end cell cell 1 minus 8 plus 7 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 equals straight O Now comma space space space space space space space straight f space left parenthesis straight A right parenthesis space equals straight O rightwards double arrow space space space straight A squared space minus 4 straight A plus 7 straight I subscript 2 space equals 0 space space space... left parenthesis 1 right parenthesis rightwards double arrow space space space straight A squared space minus 4 straight A plus 7 straight I subscript 2 rightwards double arrow space space space straight A cubed minus 4 straight A squared plus 7 straight I subscript 2 space straight A rightwards double arrow space space space straight A cubed minus 4 left parenthesis 4 straight A plus 7 straight I subscript 2 space right parenthesis minus 7 straight A space space space space space space open square brackets table row cell because space of end cell cell left parenthesis 1 right parenthesis end cell end table close square brackets rightwards double arrow space space space straight A cubed minus 9 straight A plus 282 straight I subscript 2 space rightwards double arrow space space space straight A cubed minus 9 straight A squared minus 28 straight A space equals space 9 space left parenthesis 4 straight A minus space 7 space straight I subscript 2 space right parenthesis space minus 28 straight A space space open square brackets table row cell because space of end cell cell left parenthesis 1 right parenthesis end cell end table close square brackets rightwards double arrow space space space straight A cubed minus 36 straight A minus 63 straight I subscript 2 space minus space 28 space straight A equals space 8 straight A minus 63 space straight I subscript 2 rightwards double arrow space space space straight A cubed minus 8 straight A squared minus 63 straight A rightwards double arrow space space space straight A to the power of 5 equals 8 left parenthesis 4 straight A minus 7 straight I subscript 2 right parenthesis minus 63 straight A equals space minus 31 straight A minus 56 space straight I subscript 2 rightwards double arrow space space space straight A to the power of 5 minus 31 space open square brackets table row 2 3 row 1 2 end table close square brackets minus 56 space open square brackets table row 1 cell space 0 end cell row 0 cell space space 1 end cell end table close square brackets rightwards double arrow space space space straight A to the power of 5 space equals space open square brackets table row cell negative 62 end cell cell negative 93 end cell row 31 cell negative 62 end cell end table close square brackets plus space open square brackets table row cell negative 56 end cell cell space space 0 end cell row 0 cell space space minus 56 end cell end table close square brackets space space space rightwards double arrow space space space straight A to the power of 5 space equals open square brackets table row cell negative 118 end cell cell space minus 93 end cell row 31 cell space space minus 118 end cell end table close square brackets space

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