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Relations and Functions

Short Answer Type

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

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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

We arc given that

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

From the definition of equality of matrices, we have
x+ 2y = 0        -(I)
3.y= – 3    ...(2)
4 x =8     ...(3)
From (2),    y = – 1
From (3).    x = 2
Also (1) is satisfied for ,x = 2. y = – 1 we have x = 2. y= – 1

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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

134 Views

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

134 Views

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Short Answer Type

324. find the values of x and y