ss_10_5

# ss_10_5 - Section 10.5 Matrix Algebra In this section we...

This preview shows pages 1–3. Sign up to view the full content.

Section 10.5 Matrix Algebra In this section, we deﬁne matrix operations such as addition, subtraction, and multiplication, and we give a procedure for ﬁnding the inverse of intertible matrices. A matrix is a rectangular array of numbers. A matrix that has m rows and n columns is said to be an m × n matrix, and the m × n matrix is said to be of order m × n . The element a ij is in row i and column j of the matrix ( a ij ). ( a ij )= a 11 a 12 ··· a 1 j a 1 n a 21 a 22 a 2 j a 2 n a i 1 a i 2 a ij a in a m 1 a m 2 a mj a mn Examples of matrices. ± 12 - 1 3 - 22 ² - 13 24 1 - 10 21 2 341 7 Matrix Equality. Two matrices A =( a ij )and B b ij ) are equal iﬀ a ij = b ij for all i, j . Note: Two matrices are equal iﬀ corresponding entries are identical. Example. ± 34 ² = ³ ´± 21 ² 6 = ± ² Adding and Subtracting Matrices Only matrices of the same order can be added and subtracted. Matrices are added and sub- tracted term by term, i.e., if A a ij B b ij ), then A + B a ij + b ij A - B a ij - b ij ). Example. If A = ± 11 - 23 ² and B = ± 20 - 47 ² ,then A + B = ± 31 - 61 0 ² A - B = ± - 2 - 4 ² Let α be a scalar and let A a ij ) be a matrix. Then scalar multiplication is deﬁned by αA αa ij ). Example. Let α =2and A = ± - ² .Th en αA =2 ± - ² = ± - 46 ² Some Properties of matrix addition 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A + B = B + A A +( B + C )=( A + B )+ C ( k + h ) A = kA + hA k ( A + B )= + kB Multiplication of Matrices The 1 × n matrix R =[ r 1 ,r 2 , ··· n ] is called a row vector .Th e m × 1 matrix C = c 1 c 2 .
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

### Page1 / 6

ss_10_5 - Section 10.5 Matrix Algebra In this section we...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online