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## Linear algebra

### Course: Linear algebra>Unit 2

Lesson 6: More determinant depth

# Determinant when row multiplied by scalar

The determinant when a row is multiplied by a scalar. Created by Sal Khan.

## Want to join the conversation?

• At Why is the cofactor determinant of f equal to (dh-eg) and not (ah-bg)? I might have misunderstood the pattern.
• You are correct; Sal made a mistake there.
• Do the same rules for the determinant when a row is multiplied by a scalar apply to when a column is multiplied by a scalar?
• Yes. If you transpose a matrix its determinant doesn't change so you can consider multiplying a column by a scalar as first transposing the matrix, then multiplying the equivalent row by the scalar.
• Do these rules apply for a m by n matrix?
• The determinant isn't defined for non-square matrices because non-square matrices aren't invertible in the traditional sense.
• at ~, sal is writing out 3rd/final term of the 3x3 determinant |A|...but shouldn't it be "-f(ah-bg)" vs "-f(dh-eg)" ?
• Yes. Transcription error from a few minutes in. [I'm writing words to pass the comment screener.]
(1 vote)
• Can anyone tell me why in 3*3 matrix determinant is of order + - + -...? What is its proof? I am talking about the cofactor. Where does the cofactor emerge from?
• How would we use the Anxn formula in finding the determinant for example a 4x4 matrice? Can somebody tell me what values to place in i and j? And how will we find the determinant of Aij in this case?
• How to multiply 4m+ 3n = 1 by 8/x - 9/y = 7 ?
• Okay,

If we make that substitution we get the two equations 4m+3n=1 and 8m-9n=7. Lets solve it by solving the first equation for m to get m=(1-3n)/4 and then substitution that into the second to get 8((1-3n)/4)-9n=7. This simplifies to 2-15n=7. Solving for n gives us n=-1/3. Then we remember we have m=(1-3n)/4=1/2.
(1 vote)
• At , shouldn't he have written
| a b |
| g h |?