Higher Engineering Mathematics, Sixth Edition
242 Higher Engineering Mathematics Thus ( x y ) = ⎛ ⎜ ⎜ ⎝ 21 29 + 95 29 28 29 − 57 29 ⎞ ⎟ ⎟ ⎠ i.e. ( x y ) = ( 4 − 1 ) (v) By co ...
The solution of simultaneous equations by matrices and determinants 243 ⎛ ⎝ 100 010 001 ⎞ ⎠× ⎛ ⎝ x y z ⎞ ⎠= 1 35 × ⎛ ⎝ ( 14 × 4 ...
244 Higher Engineering Mathematics Dy= ∣ ∣ ∣ ∣ ∣ a 1 c 1 a 2 c 2 ∣ ∣ ∣ ∣ ∣ i.e. the determinant of the coefficients left when th ...
The solution of simultaneous equations by matrices and determinants 245 Following the procedure: (i) ( 9 +j 12 )I 1 −( 6 +j 8 )I ...
246 Higher Engineering Mathematics DI 1 = ∣ ∣ ∣∣ ∣ ∣ 3 − 4 − 26 − 5 − 387 26 − 12 ∣ ∣ ∣∣ ∣ ∣ =( 3 ) ∣ ∣ ∣ ∣ − 387 6 − 12 ∣ ∣ ∣ ∣ ...
The solution of simultaneous equations by matrices and determinants 247 Kirchhoff’s laws are used to determine the current equa ...
248 Higher Engineering Mathematics Hence x= Dx D = 70 35 = 2 ,y= Dy D = − 105 35 =− 3 and z= Dz D = 175 35 = 5 Now try the follo ...
The solution of simultaneous equations by matrices and determinants 249 Use the Gaussian elimination method to solve for I 1 ,I ...
Revision Test 7 This Revision Test covers the material contained in Chapters 20 to 23.The marks for each question are shown in b ...
Chapter 24 Vectors 24.1 Introduction This chapter initially explains the difference between scalar and vector quantities and sho ...
252 Higher Engineering Mathematics An arrow is used to denote the sense, or direction, of the vector. The arrow end of a vector ...
Vectors 253 (ii) A lineabis constructed which is parallel to and equal in length to 0 c. (iii) The resultant force is given by t ...
254 Higher Engineering Mathematics Thus,the resultant of the two force vectors is 18N at 34 ◦to the 15N force. 10N R 15N Figur ...
Vectors 255 From trigonometry (see Chapter 11), cosθ= 0 a 0 b from which, 0a= 0 bcosθ =Fcosθ i.e. the horizontal component ofF=F ...
256 Higher Engineering Mathematics A method of adding two vectors together is to use horizontal and vertical components. The hor ...
Vectors 257 10N 15N Figure 24.22 The horizontal component of the 15N force is 15cos0◦ and the horizontal component of the 10N fo ...
258 Higher Engineering Mathematics Thus,the resultant of the two accelerations is a single vector of 31.76m/s^2 at 118. 18 ◦to t ...
Vectors 259 resultant of the two forces, and the direc- tion of the resultant with respect to the 12N force. [17.35N at 18. 00 ◦ ...
260 Higher Engineering Mathematics 158 458 2 m/s 4 m/s 3.5 m/s 308 Figure 24.32 An object is acted uponby twoforces of mag- nit ...
Vectors 261 R 2 2.13 0 2.99 Figure 24.36 Horizontal component ofa 1 −a 2 = 1 .5cos90◦− 2 .6cos145◦=2.13 Vertical component o ...
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