If a square matrix A is such that A-5 and 2A-640- then the order of A is -2 marks-

Given : nbsp;|A|=5 and |2A|=640 We know that (k A)=k^n|A|, where n is the order of matrix A and k∈ℝ ⇒ |2A|=2^n·|A|=640 ⇒ 2^n=6405 ⇒ 2^n=128=2^7 ∴ n=7 ...

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Scalar Matrix

If a square m...

Question

If a square matrix $A$ is such that $det (A) = 5$ and $det (2 A) = 640,$ then the order of $A$ is

[2 marks]

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Solution

The correct option is C $7$
Given : $| A | = 5$ and $| 2 A | = 640$
We know that $det (k A) = k^{n} | A |,$ where $n$ is the order of matrix $A$ and $k \in R$
$\Rightarrow | 2 A | = 2^{n} \cdot | A | = 640$
$\Rightarrow 2^{n} = \frac{640}{5}$
$\Rightarrow 2^{n} = 128 = 2^{7}$
$∴ n = 7$

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If a square matrix A is such that det(A)=5 and det(2A)=640, then the order of A is [2 marks]

The correct option is C 7Given : |A|=5 and |2A|=640 We know that det(kA)=kn|A|, where n is the order of matrix A and k∈R ⇒|2A|=2n⋅|A|=640 ​​⇒2n=6405 ⇒2n=128=27 ∴n=7

If a square matrix $A$ is such that $det (A) = 5$ and $det (2 A) = 640,$ then the order of $A$ is

[2 marks]

The correct option is C $7$
Given : $| A | = 5$ and $| 2 A | = 640$
We know that $det (k A) = k^{n} | A |,$ where $n$ is the order of matrix $A$ and $k \in R$
$\Rightarrow | 2 A | = 2^{n} \cdot | A | = 640$
$\Rightarrow 2^{n} = \frac{640}{5}$
$\Rightarrow 2^{n} = 128 = 2^{7}$
$∴ n = 7$