Find det(2A) if det(A)=3
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Find det(2A) if det(A)=3

[From: ] [author: ] [Date: 11-11-06] [Hit: ]
the 2x2 identity matrix)-Let Abe nxn matrix.determinant is a sum of all possible products of elements not belonging to same row or column. I every term there are n distinct elements of the matrix. In 2A as every element gets multiplied by 2. in det(2A), every term in detA,......
I think the answer is 6, but this seems way too simple...

am i missing something?

can you please tell me how to solve this, thanks!

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if you multiply one row of A by 2, then the determinant doubles.
if you multiply all the rows by 2, then the factor is 2^n, if A is an nxn matrix.
so the answer will be 3 * 2^n

(try it out with a 2x2 matrix, e.g. the 2x2 identity matrix)

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Let Abe nxn matrix.
det(A) = 3
determinant is a sum of all possible products of elements not belonging to same row or column. I every term there are n distinct elements of the matrix. In 2A as every element gets multiplied by 2. in det(2A), every term in detA, will be multiplied by 2^n. Hence
det(2A) = (2^n)*3

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You need to know the dimension of the matrix.
The answer is 2ⁿ * det(A) where n = the number of rows.
When you multiply a row by a constant k, the resulting det(B) = k * det(A).
Hence, when you have n rows, det(B) = kⁿ * det(A).

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we can't give answer without knowing order of A .If it has order n then answer is 2^n * det(A).Because 2A means we multiply 2 for every row or column , so we get n 2's in common.
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