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Maths-

General

Easy

Question

If A = $open square brackets table row 1 alpha row 0 1 end table close square brackets$ , then A⁴ is equal to-

$[\begin{matrix} 1 & α^{4} \\ 0 & 1 \end{matrix}]$
$[\begin{matrix} 4 & 4 α \\ 0 & 4 \end{matrix}]$
$[\begin{matrix} 4 & α^{4} \\ 0 & 4 \end{matrix}]$
$[\begin{matrix} 1 & 4 α \\ 0 & 1 \end{matrix}]$

hint Hint:

Suppose we have two matrices A and B, the multiplication of matrix A with Matrix B can be given as (AB). That means, the resultant matrix for the multiplication of for any m × n matrix 'A' with an n × p matrix 'B', the result can be given as matrix 'C' of the order m × p. Let us understand this concept in detail in the next section.

The correct answer is: $open square brackets table row 1 cell 4 alpha end cell row 0 1 end table close square brackets$

Given : A = $open square brackets table row 1 alpha row 0 1 end table close square brackets$ ,

To Find : $A to the power of 4$

$rightwards double arrow A squared equals space A space. space A space rightwards double arrow A squared equals open square brackets table row cell 1 space space alpha end cell row cell 0 space space 1 end cell end table close square brackets space open square brackets table row cell 1 space space alpha end cell row cell 0 space space 1 end cell end table close square brackets equals open square brackets table row cell 1 space space 2 alpha end cell row cell 0 space space 1 end cell end table close square brackets rightwards double arrow A cubed space equals space space A squared space. space A rightwards double arrow A cubed equals open square brackets table row cell 1 space space 2 alpha end cell row cell 0 space space 1 end cell end table close square brackets space open square brackets table row cell 1 space space alpha end cell row cell 0 space space 1 end cell end table close square brackets equals open square brackets table row cell 1 space space 3 alpha end cell row cell 0 space space 1 end cell end table close square brackets rightwards double arrow A to the power of 4 equals A cubed. space A space space space space space space space space space space space space space space space space space rightwards double arrow A to the power of 4 space space equals space open square brackets table row cell 1 space space 3 alpha end cell row cell 0 space space 1 end cell end table close square brackets space open square brackets table row cell 1 space space alpha end cell row cell 0 space space 1 end cell end table close square brackets equals space open square brackets table row cell 1 space space 4 alpha end cell row cell 0 space space 1 end cell end table close square brackets rightwards double arrow A to the power of 4 equals space open square brackets table row cell 1 space space 4 alpha end cell row cell 0 space space 1 end cell end table close square brackets$

Related Questions to study

If A = $open square brackets table row 0 1 row 0 0 end table close square brackets$ , I is the unit matrix of the order two & a, b are arbitrary constant then
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parallel

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