To determine The value of the expressions ( 5 u + 5 v ) − 1 2 w , − 20 ( u + v ) + 2 w , E − ( u + v ) , 10 ( u + v ) + w . Explanation Given: The matrices are A = [ 0 2 4 6 5 5 1 0 − 3 ] , B = [ 0 5 2 5 3 4 − 2 4 − 2 ] , C = [ 5 2 − 2 4 1 0 ] , D = [ − 4 1 5 0 2 − 1 ] , E = [ 0 2 3 4 3 − 1 ] , u = [ 1.5 0 − 3 ] , v = [ − 1 3 2 ] , w = [ − 5 − 30 10 ] . Definition used: “Addition of two matrices: The sum of two matrices A = [ a j k ] and B = [ b j k ] of the same size is written A + B and has the entries a j k + b j k obtained by adding the corresponding entries of A and B . Matrices of different sizes cannot be added. Multiplication of matrices: The product of any m × n matrix A = [ a j k ] and any scalar c is written c A and is the m × n matrix c A = [ c a j k ] obtained by multiplying each entry of A by c.” Rules used: 1. A + B = B + A 2. ( A + B ) + C = A + ( B + C ) 3. A + 0 = A 4. A + ( − A ) = 0 5. c ( A + B ) = c A + c B 6. ( c + k ) A = c A + k A 7. c ( k A ) = ( c k ) A 8. 1 A = A Calculation: From the above definition, the value of the expression ( 5 u + 5 v ) − 1 2 w is, ( 5 u + 5 v ) − 1 2 w = ( 5 [ 1.5 0 − 3 ] + 5 [ − 1 3 2 ] ) − 1 2 [ − 5 − 30 10 ] = ( [ 7.5 0 − 15 ] + [ − 5 15 10 ] ) − [ − 2.5 − 15 5 ] = [ 2

Custom Kreyszig: Advanced Engineering Mathematics

10th Edition

ISBN: 9781119166856

Author: Kreyszig

Publisher: JOHN WILEY+SONS INC.CUSTOM

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Chapter 7.1, Problem 14P

To determine

The value of the expressions (5u+5v)−12w,−20(u+v)+2w,E−(u+v),10(u+v)+w.

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Chapter 7.1, Problem 13P

Chapter 7.1, Problem 15P

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Custom Kreyszig: Advanced Engineering Mathematics

Ch. 7.1 - Equality. Give reasons why the five matrices in...Ch. 7.1 - Double subscript notation. If you write the matrix...Ch. 7.1 - Sizes. What sizes do the matrices in Examples 1,...Ch. 7.1 - Main diagonal. What is the main diagonal of A in...Ch. 7.1 - Scalar multiplication. If A in Example 2 shows the...Ch. 7.1 - If a 12 × 12 matrix A shows the distances between...Ch. 7.1 - Addition of vectors. Can you add: A row and a...Ch. 7.1 - Let Find the following expressions, indicating...Ch. 7.1 - Let Find the following expressions, indicating...Ch. 7.1 - Let Find the following expressions, indicating...

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