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Matrices

Short Answer Type

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

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

Here

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

Now, A = B

$rightwards double arrow space space space space open square brackets table row cell 2 straight x plus 1 end cell cell 3 straight y end cell row 0 cell straight y squared minus 5 straight y end cell end table close square brackets equals open square brackets table row cell straight x plus 3 end cell cell straight y squared plus 2 end cell row 0 cell negative 6 end cell end table close square brackets$

∴ by the definition of equality of matrices.
2 x + 1 = .x + 3, 3 y = + 2 , y² –5 y = – 6
Now 2 x + I = x + 3 ⇒ x= 2
3 x = y² +2 ⇒ y² -3 y + 2 = 0 ⇒ ( y –1) (y – 2) = 0 ⇒ y = I, 2
y²–5 y =-6 ;⇒ -5 y + 6 = 0 ;⇒ (y–2)(y–3) = 0 ;⇒ y = 2.3
Since both the equations 3 y = y² +2 and y² –5 y = – 6 arc to be satisfied
simultaneously, so we have y = 2.
∴A – B when x = 2, y – 2.

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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.

94 Views

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
$straight y equals 7 comma space space space straight x equals fraction numerator negative 2 over denominator 3 end fraction$
$straight y equals 7 comma space space space straight x equals fraction numerator negative 2 over denominator 3 end fraction$

95 Views

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.