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If A is a matrix of order 4 and |A| = 12, what is the value of the determinant of the matrix obtained by multiplying every entry in A by 2?

A) 12
B) 24
C) 48
D) 96

User Elzbieta
by
8.4k points

1 Answer

3 votes

Final answer:

The determinant of the matrix obtained by multiplying every entry in a 4x4 matrix A by 2 is 192, which is found by multiplying the original determinant by 2 to the power of 4.

Step-by-step explanation:

When a matrix A of order 4 (which means it is a 4x4 matrix) has a determinant value of |A| = 12, and you multiply every entry in the matrix by 2, you need to understand what happens to the determinant. For every row that you multiply by a constant (in this case, 2), the determinant of the matrix gets multiplied by that constant. Since there are four rows in a 4x4 matrix, you will multiply the original determinant (12) by 2 four times. Therefore, the determinant of the new matrix will be 2^4 times the original determinant |A|.

2^4 * 12 = 16 * 12 = 192. So, the value of the determinant of the matrix obtained by multiplying every entry in A by 2 is 192.

This question does not match the reference information provided. Hence, the answer has been determined based on the given mathematical principles

User Antoine Floury
by
8.3k points
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