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Matrices

Short Answer Type

31. For what values of ,x and y are the following matrices equal 7

straight A equals open square brackets table row cell 2 straight x plus 1 end cell cell 3 straight y end cell row 0 cell straight y squared minus 5 straight y end cell end table close square brackets comma space space straight B equals open square brackets table row cell straight x plus 3 end cell cell straight y squared plus 2 end cell row 0 cell negative 6 end cell end table close square brackets

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32.
If $open square brackets table row cell straight x minus straight y end cell straight z row cell 2 straight x minus straight y end cell straight w end table close square brackets equals open square brackets table row cell negative 1 end cell 4 row 0 5 end table close square brackets$ find .x. y. z .w.

We are given that

$open square brackets table row cell straight x minus straight y end cell straight z row cell 2 straight x minus straight y end cell straight w end table close square brackets equals open square brackets table row cell negative 1 end cell 4 row 0 5 end table close square brackets$

From the definition of equality of matrices, we have
x –y = –1    ..(I)
2.x–y=0    ...(2)
z = 4    ...(3)
w = 5     ..(4)
Subtracting (1) from (2). we get,
x= 1
∴from (1). I -y = –l ⇒ y = 2
∴.x – 1. y = 2. z =-4. w- = 5

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Multiple Choice Questions

33. Which of the given values of x and y make the following pair of matrices equal

open square brackets table row cell 3 straight x plus 7 end cell 5 row cell straight y plus 1 end cell cell 2 minus 3 straight x end cell end table close square brackets. open square brackets table row 0 cell straight y minus 2 end cell row 8 4 end table close square brackets

$straight x equals fraction numerator negative 1 over denominator 3 end fraction comma space space straight y space equals 7$
Not possible to find
$straight y equals 7 comma space space space straight x equals fraction numerator negative 2 over denominator 3 end fraction$
$straight y equals 7 comma space space space straight x equals fraction numerator negative 2 over denominator 3 end fraction$

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34.

A - {a._{i j} ]_{m x n} is a square matrix, if

m < n
m > n
m = n
m = n

98 Views

35.

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is.

217 Views

Short Answer Type

36.

If $straight A equals open square brackets table row 2 4 row 3 2 end table close square brackets space and space straight B equals open square brackets table row cell space 1 end cell 3 row cell negative 2 space end cell 5 end table close square brackets$ then find A – B.

151 Views

37.

Given $straight A equals open square brackets table row cell square root of 3 end cell 1 cell negative 1 end cell row 2 3 0 end table close square brackets space and space straight B equals open square brackets table row 2 cell square root of 5 end cell 1 row cell negative 2 end cell 3 cell 1 half end cell end table close square brackets$ , Find A + B.

103 Views

38.

If $straight A equals open square brackets table row 2 3 cell negative 4 end cell row 1 0 6 row cell negative 2 end cell 1 5 end table close square brackets comma space straight B equals open square brackets table row 5 1 2 row 6 cell negative 1 end cell 4 row 5 3 cell negative 4 end cell end table close square brackets$ , find 2A - 3B.