Question

How does he work out the I1 I2 I3 I4 values

can you show the working and steps
For mesh (1) [ 26 I₁ - 12 I₂ + 0 I₃ - 6 I₄ = -15 ]
For mesh (2) [ -12 I₁ + 21 I₂ - 5 I₃ +4 I₄ = 0 ]
For mesh (3) [ 0 I₁ - 5 I₂ + 19 I₃ + 0 I₄ = 0 ]
For mesh(4) [ -6 I₁ - 4 I₂ + 0 I₃ + 15 I₄ = 0]

using matrices
[(26, -12, 0, -6) (-12, 21, -5, -4)(0, -5, 14, 0)(-6, -4, 0, 15)][I₁, I₂, I₃, I₄] = [-15, 0, 0, 0 ]

Answer 1

To find the values of I1, I2, I3, and I4, rewrite the given equations in matrix form and solve the system using the inverse of the coefficient matrix. The values of I1, I2, I3, and I4 are 28.5 - 51, 6 - 21(28.5 - 51), 22.5 - 31(28.5 - 51), and 0 respectively.

Step-by-step explanation:

First, let's rewrite the given equations in matrix form:

[26 -12 0 -6] [I₁] = [-15]

[-12 21 -5 -4] [I₂] = [0]

[0 -5 14 0] [I₃] = [0]

[-6 -4 0 15] [I₄] = [0]

Next, we can solve the system of linear equations by multiplying the inverse of the coefficient matrix on both sides:

[I₁] = [28.5 -51] (where I₂ = 6 - 21I₁ and I₃ = 22.5 - 31I₁)

Therefore, the values of I₁, I₂, I₃, and I₄ are 28.5 - 51, 6 - 21(28.5 - 51), 22.5 - 31(28.5 - 51), and 0 respectively.