step 1 So in the given question we have a matrix A which is said to be a square matrix. It is a square

Question

$$ \text { (a) } 25|\mathrm{~A}| $$

Name: Problem 34, Chapter 2: IIT JEE Super Course in Mathematics ALGEBRA II
Uploaded: 2021-06-24T08:20:43-08:00
Duration: 2 min 17 s
Channel: Anas Venkitta
Description: (a) 25| A|

   $$
\text { (a) } 25|\mathrm{~A}|
$$

IIT JEE Super Course in Mathematics ALGEBRA II

Trishna Knowledge… 2011 Edition

Chapter 2, Problem 34

Instant Answer

Solved by Expert Anas Venkitta

06/24/2021

Step 1

Step 1: We are given a square matrix A of order 5 and we are asked to find the determinant of 5 times A. Show more…

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$$ \text { (a) } 25|\mathrm{~A}| $$

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Key Concepts

Determinant

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides crucial information about the matrix, such as whether it is invertible, and measures the scaling factor of the linear transformation associated with the matrix. The determinant is commonly denoted by vertical bars around the matrix, such as |A|, and is fundamental in solving systems of linear equations and understanding eigenvalues.

Scalar Multiplication in Determinants

Scalar multiplication in the context of determinants refers to the effect of multiplying a matrix by a constant factor. When a matrix is scaled, its determinant is multiplied by that scalar raised to the power corresponding to the matrix's order. This property helps in understanding how the overall scaling of a linear transformation changes when the matrix is adjusted by a constant factor.

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