Easy matrix/determinants question

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In summary, using the given information, we can find that det C = y/(8x), which is not one of the solutions given.
  • #1
astonmartin
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Homework Statement



Suppose A and B are 3 x 3 matrices and det A = x ≠ 0 while det B = y. Let
C be the matrix ((2A)^-1 )B <-- (2A) inverse x B

then det C is:

Homework Equations

The Attempt at a Solution



det(2A) = 2x, so det 2A inverse = 1/(2x)
det C = y/(2x)...which is not one of the solutions

a) y/8x b) 2xy c) -2y/x d) 2y/x e) 8y/x

what am I missing here?
 
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  • #2
You are very close; however,

[tex]\det(\alpha A)=\alpha^{n} \det(A)[/tex]

where n is the order of the matrix A, in this case 3. To understand why this happens, think of the determinant of the identity and multiply it by a scalar.
 

Related to Easy matrix/determinants question

What is a matrix and how is it used in mathematics?

A matrix is a rectangular array of numbers or symbols that are arranged in rows and columns. It is used in mathematics to represent and solve systems of equations, transformations, and other mathematical operations.

What is a determinant and what is its significance in matrix operations?

A determinant is a numerical value that is calculated from the elements of a square matrix. It is significant in matrix operations because it can determine whether a matrix has a unique solution, and it is also used to find the inverse of a matrix.

How do you calculate the determinant of a 2x2 matrix?

The determinant of a 2x2 matrix is calculated by multiplying the elements in the main diagonal and subtracting the product of the elements in the other diagonal. For example, the determinant of the matrix [a b; c d] is ad - bc.

What is the relationship between the determinant and the area/volume of a shape?

The absolute value of the determinant of a 2x2 matrix represents the area of the parallelogram formed by the column vectors of the matrix. Similarly, the absolute value of the determinant of a 3x3 matrix represents the volume of the parallelepiped formed by the column vectors of the matrix.

Can the determinant of a matrix be negative?

Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the arrangement of the elements in the matrix and does not affect its numerical value.

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