Construct a 3 x 4 matrix, whose elements are given by : from Ma

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Relations and Functions

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321. Construct a 3 x 4 matrix, whose elements are given by :

$straight a subscript straight i space straight j end subscript equals 1 half space vertical line space minus 3 space straight i space plus space straight j right square bracket$

Let A = [a_{i j} be required 3x4 matrix where

a subscript i j equals 1 half vertical line minus 3 space i space plus space j space i vertical line end subscript

therefore space space space space straight a subscript 11 equals 1 half space space left square bracket space minus 3 plus 1 right square bracket space equals 1 half left parenthesis 2 right parenthesis equals 1 comma space space straight a subscript 12 equals 1 half vertical line minus 3 plus 2 vertical line equals 1 half left parenthesis 1 right parenthesis equals 1 half space space space space space space straight a subscript 13 equals 1 half vertical line minus 3 plus 3 vertical line equals 1 half left parenthesis 0 right parenthesis equals 0. space straight a subscript 14 equals 1 half vertical line minus 3 space plus space 4 vertical line equals 1 half left parenthesis 1 right parenthesis equals 1 half space space space space space space straight a subscript 21 equals 1 half space vertical line minus 6 plus 2 vertical line equals 1 half left parenthesis 5 right parenthesis equals 5 over 2. straight a subscript 22 equals 1 half space vertical line minus 6 plus 2 right curly bracket equals 1 half left parenthesis 4 right parenthesis equals 2 space space space space space space straight a subscript 23 equals 1 half space vertical line minus 6 minus 3 vertical line equals 1 half left parenthesis 3 right parenthesis equals 3 over 2. space straight a subscript 24 equals 1 half space vertical line minus 6 plus 4 vertical line equals 1 half left parenthesis 7 right parenthesis equals 7 over 2 space space space space space space straight a subscript 33 equals 1 half space vertical line minus 9 plus 3 vertical line space equals space 1 half space left parenthesis 6 right parenthesis space equals 3. space straight a subscript 34 equals 1 half space vertical line minus 9 plus 4 vertical line equals 1 half left parenthesis 5 right parenthesis equals 5 over 2 therefore space space straight A equals open square brackets table row 1 cell 1 half end cell 0 cell 1 half end cell row cell 5 over 2 end cell 2 cell 3 over 2 end cell 1 row 4 cell 7 over 2 end cell 3 cell 5 over 2 end cell end table close square brackets

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322. Construct a 3 x 4 matrix, whose elements are given by :

straight a subscript straight i space straight j end subscript equals 1 half space vertical line space minus 3 space straight i space plus space straight j right square bracket

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323.

If space open square brackets table row cell straight x plus 2 straight y space space end cell cell negative straight y end cell row cell 3 straight x end cell 4 end table close square brackets equals open square brackets table row cell negative 4 end cell 3 row 6 4 end table close square brackets

find the values of .x and y.

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324.

If space open square brackets table row cell straight x plus 2 straight y space space end cell cell 3 straight y end cell row cell 4 straight x end cell 2 end table close square brackets equals open square brackets table row 0 cell space minus 3 end cell row 8 cell space space space 2 end cell end table close square brackets

find the values of x and y

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325.

If space open square brackets table row cell straight x minus straight x end cell cell 2 straight x plus straight z end cell row cell 2 straight x minus straight y end cell cell 3 straight z plus straight w end cell end table close square brackets equals open square brackets table row cell negative 1 end cell 5 row 0 13 end table close square brackets

find x. y. z. w.

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326. Find the values of.x, y and z from the following equations :

open square brackets table row cell straight x plus straight y space space space space end cell 2 row cell 5 plus straight z space space space space end cell cell straight x space straight y end cell end table close square brackets equals space open square brackets table row 6 2 row 5 8 end table close square brackets

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327. Find the values of.x, y and z from the following equations :

open square brackets table row cell x plus y plus z end cell row cell x plus z end cell row cell y plus z end cell end table close square brackets equals open square brackets table row 9 row 5 row 7 end table close square brackets

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328. Find the values of a. b, c and rf from the equation :

open square brackets table row cell straight a minus straight b space space space space space space space space space space end cell cell 2 straight a plus straight c end cell row cell 2 straight a minus straight b space space space space space space space space space end cell cell 3 straight c plus straight d end cell end table close square brackets equals open square brackets table row cell negative 1 end cell 5 row 0 13 end table close square brackets

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329.

If space open square brackets table row straight x cell 3 straight x minus straight y end cell row cell 2 straight x plus straight z end cell cell 3 straight y minus straight w end cell end table close square brackets equals open square brackets table row 3 2 row 4 7 end table close square brackets

find x, y, x, w'

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330. Find ,x, y , a and b if

open square brackets table row cell 2 straight x minus 3 straight y end cell cell straight a minus straight b end cell 3 row 1 cell straight x plus 4 straight y end cell cell 3 straight a plus 4 straight b end cell end table close square brackets equals open square brackets table row 1 cell negative 2 end cell 3 row 1 6 29 end table close square brackets

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