If a square matrix A is such that A-5 and 2A-320- then the order of A is

Name: JEE- Grade 12- Mathematics- Matrices and Determinants- Session 05- D09
Uploaded: 2022-07-04T10:36:42+05:30
Description: We know, (K· A)=K^n·|A| ⇒(2· A)=320=2^n·5 ⇒ 2^n=64 ∴ n=6 ...

We know, (K· A)=K^n·|A| ⇒(2· A)=320=2^n·5 ⇒ 2^n=64 ∴ n=6 ...

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Standard X

Mathematics

Scalar Matrix

If a square m...

Question

If a square matrix $A$ is such that $det (A) = 5$ and $det (2 A) = 320$ , then the order of $A$ is

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Solution

We know, $det (K \cdot A) = K^{n} \cdot | A |$
$\Rightarrow det (2 \cdot A) = 320 = 2^{n} \cdot 5$
$\Rightarrow 2^{n} = 64$
$∴ n = 6$

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If a square matrix A is such that det(A)=5 and det(2A)=320, then the order of A is

We know, det(K⋅A)=Kn⋅|A| ⇒det(2⋅A)=320=2n⋅5 ⇒2n=64 ∴n=6

If a square matrix $A$ is such that $det (A) = 5$ and $det (2 A) = 320$ , then the order of $A$ is

We know, $det (K \cdot A) = K^{n} \cdot | A |$
$\Rightarrow det (2 \cdot A) = 320 = 2^{n} \cdot 5$
$\Rightarrow 2^{n} = 64$
$∴ n = 6$