Friday

February 27, 2015

February 27, 2015

Posted by **Vidal** on Sunday, June 10, 2007 at 2:15pm.

b) Show that your formula from (a) is true for all n and for any k.

det (kB) = k^n det B

This is because the determinant is a multilinear function of it's columns (or rows) considered as vectors to the reals. If you multiply one particular colomn of the matrix by k, then the entire determinat get's multiplied by k.

So, if you muliply the whole matrix by k, then that amounts to multiplying each column by k, and thus the determinant picks up a factor k^n.

**Answer this Question**

**Related Questions**

Algebra - A is a 2 by 2 matrix. Given that A=(5 1) (1 5) , what is the value of ...

Linear Algebra - Suppose C and D and 5x5 matrices and det(C)=5, det(D)=6. ...

Math (matrices) - No one answered my matrix question. Let me rephrase: Let A, B...

Math: determinants - If det(A)=-7 A= | a b c | | d e f | | g h i | Find det(2A^-...

algebra 2 - find the inverse of A, recall that A-1 = 1/det A [d -b] [ -c a]

social studies - what are detors called when they work to pay off there det?

Maths - Matrices - Matrix transformations- please help? let f be the linear ...

algebra - solve system graphically. be sure to check your solution. if a system ...

math - tim has a det of $872.23. If he pays 40 percent of the debt this month ...

algebra - Can anyone help explain how to work this problem out? One factor in ...