Find the determinants in Exercise , assuming that begin{vmatrix}a & b &c d&e&fg&h&i end{vmatrix}=4 begin{vmatrix}2a & 2b &2c d&e&fg&h&i end{vmatrix}

Cabiolab 2020-12-07 Answered
Find the determinants in Exercise , assuming that
|abcdefghi|=4
|2a2b2cdefghi|
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Expert Answer

Macsen Nixon
Answered 2020-12-08 Author has 117 answers
Step 1
Determinant is used for solving linear equations. To find the inverse of a matrix determinant is used. It is computed only for square matrices. Square matrices are matrices whose number of rows and number of columns are equal.
Step 2
The given value of the determinant is |abcdefghi|=4 Multiplying any row or column of a determinant by a number x, multiplies the determinant by that number x. Using this property the value of the determinant |2a2b2cdefghi| is calculated by taking the common term 2 from the first row and take the value 2 outside of the determinant, then it becomes 2 times of the determinant |abcdefghi| , using the value given value find the asked determinant value as follows,
|abcdefghi|=4
|2a2b2cdefghi|=|2×a2×b2×cdefghi|
=2|abcdefghi| Take the coomon term from first row outside of determinant. =2×4 Subtitute |abcdefghi|=4
=8
Hence, the value of the determinant asked in the question is equal to
|2a2b2cdefghi|=8
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Jeffrey Jordon
Answered 2022-01-24 Author has 2047 answers

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