[PDF] Matrix multiplication

Example of multiplying matrices 2 0 −5 −1 −4 6 −2 ×[ 0 −1 −3 2 ]= c11 c12 c21 c22 c31 c32 For the first entry c11 we multiple

Previous PDF

Next PDF

2 nov 2005 · (a) 26, (b) −26, (c) −12, (d) 12 If A and B are two matrices, the product AB can be found if the number of columns of A equals the number of rows of B If A is 2 × 3 and B is 3×5 then AB can be calculated but BA does not exist The order in which matrices are multiplied together matters

[PDF] Multiplying matrices 1 - Mathcentre

Matrix multiplication is based on combining rows from the first matrix Example Find the product ( 3 7 4 5 \ ( 2 9 \ Solution The first matrix has size 2×2

[PDF] Matrix Multiplication

The product A · B or AB of two matrices A and B is found by using the above algorithm to multiply each row of A times each column of B For example, if matrix A

[PDF] Matrix Multiplication - Learn

This matrix product is easily generalised to other row and column matrices For example if C is a 1 × 4 row matrix and D is a 4 × 1 column matrix: C = [ 2 − 4 3 2 ]

[PDF] 53 Multiplying matrices

/file/53_Multiplying_matrices.pdf

[PDF] Matrix multiplication - The University of Sydney

Example of multiplying matrices 2 0 −5 −1 −4 6 −2 ×[ 0 −1 −3 2 ]= c11 c12 c21 c22 c31 c32 For the first entry c11 we multiple

[PDF] 2 Matrix algebra

Matrix multiplication allows us to write a system of linear equations as a single matrix equation For example, the system 2x1 + 3x2 = 4 −x1 − 5x2 = 1

[PDF] 44 Matrices: Basic Operations - CSUN

More Examples of scalar The definition of subtract of two real numbers a and b is 1X4 row matrix multiplied by a 4X1 column matrix: Notice the manner in

[PDF] 3 Matrix Algebra and Applications - Mathematical Sciences : UTEP

In general, to multiply a matrix by a number, multiply every entry in the matrix by This amounts to changing the signs of all the entries in A For example, −

[PDF] matrix multiplication properties

[PDF] matrix operations

[PDF] matrix power

[PDF] matrix representation of graphs

[PDF] matrix row reduction

[PDF] matrix rref calculator wolfram

[PDF] matrix simultaneous equation calculator

[PDF] matrix solver

[PDF] matrix ti 89

[PDF] matrix vector multiplication c++

[PDF] mattydale bus schedule

[PDF] maurices credit card sign in comenity bank

[PDF] maury county tn school zoning map

[PDF] maury county tn zoning map

[PDF] max fg integrable

Matrixmultiplication

JackieNicholas

MathematicsLearning Centre

UniversityofSydney

c?2010Universit yofSydney

Multiplyingmatrices

WecanmultiplymatricesAandBtogethertofo rmthe product

ABprovidedthenumberof columnsinAequalsthenumberof

rowsinB. IfA= 4-13 1-29 andB= 0-5 -1-4 0-1 thenwe candefineABasAhasthreecolumns andBhasthree rows.

Multiplyingmatrices

IfA= 4-13 1-29 andB= 0-5 -1-4 thenABisnotdefined asAisa2 ×3matrix andBisa2 ×2 matrix;thenumber ofcolumnsof Adoesnotequal thenumberof rowsofB. Ontheother hand,the productBAisdefinedasthe numberof columnsofB,2,does equalthenumber ofro wsofA. Thistellsus somethingvery important;o rdermatters!! Inmostcas esAB?=BA.HereABisnotdefined whereasBAis.

Howtomultiplymatrices

Ingeneral,if Aisam×nmatrixandBisan×pmatrix,the productABwillbea m×pmatrix.

LetC=AB.Itis am×pmatrix.

Recallthatthe entryinthe ithrowandjthcolumnofC,iethe (i,j)thentryofC,iscalled c ij

Theentryc

ij isthep roductofthe ithrowofAandthejthcolumn ofBasfollo ws: c ij =a i1 b 1j +a i2 b 2j +a i3 b 3j +a i4 b 4j +···+a in b nj

Exampleofmultiplying matrices1

Thatprobably lookedabitcomplicateds owewillgothrough an example. LetA= 0-5 -1-4 6-2 andB= 0-1 -32

Aisa3 ×2matrixand Bisa2 ×2,so ABisdefined.

IfC=ABisthenC=

c 11 c 12 c 21
c 22
c 31
c 32
isa3 ×2matrix.

Exampleofmultiplying matrices2

0-5 -1-4 6-2 0-1 -32 c 11 c 12 c 21
c 22
c 31
c 32

Forthefirstentryc

11 wemultiplethefirstrowofAwiththefirst columnofBasfollows : 0-5 0. -3.

0×0+-5×-3.

iec 11 =a 11 ×b 11 +a 12 ×b 21
=15.

Exampleofmultiplying matrices3

0-5 -1-4 6-2 0-1 -32 15c 12 c 21
c 22
c 31
c 32

Fortheentryc

12 wemultiplethefirstrowofAwiththesecond columnofBasfollows : 0-5 .-1 .2 .0×-1+-5×2 iec 12 =a 11 ×b 12 +a 12 ×b 22
=-10.

Exampleofmultiplying matrices4

0-5 -1-4 6-2 0-1 -32 15-10 c 21
c 22
c 31
c 32

Fortheentryc

21
wemultiplethesecondrowofAwiththefirst columnofBasfollows : -1-4 0. -3. -1×0+-4×-3. iec 21
=a 21
×b 11 +a 22
×b 21
=12.