Category: linear algebra

Linear algebra: best fit line: method of least squares by hand

The tutor shows a nice trick to obtain a least squares line using matrix algebra. In my Nov 25 post I mentioned how, with Excel or LibreOffice Calc, to get a best-fit line for x y 0 3 2 5

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Linear algebra: matrix multiplication: no cancellation rule

The tutor gives an example to show that with matrices, AB=AC doesn’t mean B=C. Consider the matrices A, B, C, and D: By matrix multiplication, AB=AC. (In fact, both products equal D.) Yet, obviously, B≠C. Matrix multiplication lacks the cancellation

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Linear algebra: projecting a vector along another one, matrix method.

The tutor shows an example of a projection from one dimension into another. Let’s imagine we have the vector v 3 2 0 which we want to project in the direction of w 3 -1 0 The projection matrix, Pw,

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Linear algebra: cofactors, signed minors

The tutor defines cofactor (aka signed minor) with an example. In my post from Nov 24, 2014 I tell how to evaluate a determinant by hand. Example: Evaluate the determinant of matrix A: 1 0 -7 0 2 1 3

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Spreadsheets: finding the determinant of a matrix using Excel

The tutor tells how to have Excel evaluate a determinant for you. Here’s how: Key in your matrix values. Let’s imagine you use the range a1:d4. Select a cell away from the range, let’s say f6. Key in =mdeterm(a1:d4) then

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Linear Algebra: solving a three-variable linear system with Excel or LibreOffice Calc

The tutor shows an example of how to solve a system of three equations using a spreadsheet. Example: solve the system -3x + 2y + z = 16 x – y – 3z = -19 2x + y + 7z

Spreadsheets: Matrix inverse on Excel or LibreOffice Calc

The MINVERSE() function can be tricky to use; the tutor tells how. Example: find the inverse of matrix A: -5 0 1 3 8 9 0 1 0 Solution: Enter the matrix in Excel or LibreOffice Calc. Let’s imagine, for

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Linear algebra: Matrix multiplication

The tutor demonstrates the technique of multiplying matrices. To go further with Markov chains (introduced in my previous post), the reader needs to understand matrix multiplication. To many, the method is surprising at first. Example: Consider the matrices A and

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Math: Solving systems of equations: Cramer’s Rule

Tutoring high school math, I don’t see this used.  However, I did see it at university.  The tutor introduces Cramer’s Rule. Consider the following problem, common in high school math: Solve the system. 2x-4y=20 3x+5y=-3 If you know determinants (having

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Linear algebra: more on determinants

Following up on yesterday’s post, the tutor continues about determinants. Tutoring university math or natural sciences, they come up often. Yesterday’s post covered some basics about determinants including a 2×2 and a 3×3 example.  Although it revealed the necessities for

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