Tipus de Sistema

SCD

SCI

SI

Nou Sistema

 = 

 = 

 = 

 = 

 = 

 = 

 = 

 = 

 = 

solució: ∅

rang(M)=rang(M^{*})=3

Mètode de resolució

K8_1: "Si[d8 ≟ 0, " + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ", Si[abs(d8) ≠ 1, abs(D8) + " + (UnicodeToLetter[34]) + "z" + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + "z" + (UnicodeToLetter[34]) + "]]"
J8_1: "Si[D8 ≟ 0, " + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ", Si[D8 > 0, " + (UnicodeToLetter[34]) + " + " + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + " - " + (UnicodeToLetter[34]) + "]]"
I8_1: "Si[c8 ≟ 0, " + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ", Si[abs(c8) ≠ 1, abs(C8) + " + (UnicodeToLetter[34]) + "y" + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + "y" + (UnicodeToLetter[34]) + "]]"
H8_1: "Si[c8 ≟ 0, " + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ", Si[c8 > 0, " + (UnicodeToLetter[34]) + " + " + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + " - " + (UnicodeToLetter[34]) + "]]"
G8_2: "Si[b8 ≟ 0, " + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ", Si[abs(b8) ≠ 1, abs(B8) + " + (UnicodeToLetter[34]) + "x" + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + "x" + (UnicodeToLetter[34]) + "]]"
G8_1: "Si[A8 ≟ 0, " + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ", Si[abs(A8) ≠ 1, abs(b8) + " + (UnicodeToLetter[34]) + "x" + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + "x" + (UnicodeToLetter[34]) + "]]"
tipus: {"SCD", "SCI", "SI"}
H3_2: "Si[B3==0," + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ",Si[B3 > 0, " + (UnicodeToLetter[34]) + " + " + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + " - " + (UnicodeToLetter[34]) + "]]"
H3_1: "Si[B3 > 0, " + (UnicodeToLetter[34]) + " + " + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + " - " + (UnicodeToLetter[34]) + "]"
F3_1: "Si[A3 ≟ 0, " + (UnicodeToLetter[34]) + " " + (UnicodeToLetter[34]) + ", Si[A3 ≠ 1,abs( A3) + " + (UnicodeToLetter[34]) + "x" + (UnicodeToLetter[34]) + ", " + (UnicodeToLetter[34]) + "x" + (UnicodeToLetter[34]) + "]]"
A10: (-1)^(Random[1, 2])
A9 = Random(1, 4)
A8 = Random(1, 4)
B9 = Random(-5, 5)
B8 = Random(-5, 5)
B2 = Random(-5, 5)
C2 = Random(-5, 5)
A2 = Random(-5, 5)
B3_1 = 0
B3 = Random(-5, 5)
C3 = Random(-5, 5)
A3 = Random(-5, 5)
D3: (A3 * A2) + (B3 * B2) + (C3 * C2)
B4 = Random(-5, 5)
C4 = Random(-5, 5)
A4 = Random(-5, 5)
D4: (A4 * A2) + (B4 * B2) + (C4 * C2)
B5 = Random(-5, 5)
C5 = Random(-5, 5)
A5 = Random(-5, 5)
D5: (A5 * A2) + (B5 * B2) + (C5 * C2)
C8 = Random(-5, 5)
E8 = Random(-5, 5)
D8 = Random(-5, 5)
C9 = Random(-5, 5)
E9 = Random(-5, 5)
D9 = Random(-5, 5)
C10: (A8 * C8) + ((A9 * C9) * A10)
D10: (D8 * A8) + ((D9 * A9) * A10)
B10: (A8 * B8) + ((A9 * B9) * A10)
E10: (E8 * A8) + ((E9 * A9) * A10)
A15: (-1)^(Random[1, 2])
A14 = Random(1, 4)
A13 = Random(1, 4)
B14 = Random(-5, 5)
B13 = Random(-5, 5)
C13 = Random(-5, 5)
E13 = Random(-5, 5)
D13 = Random(-5, 5)
C14 = Random(-5, 5)
E14 = Random(-5, 5)
D14 = Random(-5, 5)
C15: (A13 * C13) + ((A14 * C14) * A15)
D15: (D13 * A13) + ((D14 * A14) * A15)
B15: (A13 * B13) + ((A14 * B14) * A15)
E15: (E13 * A13) + ((E14 * A14) * A15) - Random[1, 5]
p = SelectedIndex(tipus)
G3 = If(A3 ≟ 0, " ", If[abs(A3) ≠ 1, abs(A3) + "x", "x"])
I3 = If(B3 ≟ 0, " ", If[abs(B3) ≠ 1, abs(B3) + "y", "y"])
K3 = If(C3 ≟ 0, " ", If[abs(C3) ≠ 1, abs(C3) + "z", "z"])
G4 = If(A4 ≟ 0, " ", If[abs(A4) ≠ 1, abs(A4) + "x", "x"])
G5 = If(A5 ≟ 0, " ", If[abs(A5) ≠ 1, abs(A5) + "x", "x"])
I4 = If(B4 ≟ 0, " ", If[abs(B4) ≠ 1, abs(B4) + "y", "y"])
I5 = If(B5 ≟ 0, " ", If[abs(B5) ≠ 1, abs(B5) + "y", "y"])
K4 = If(C4 ≟ 0, " ", If[abs(C4) ≠ 1, abs(C4) + "z", "z"])
K5 = If(C5 ≟ 0, " ", If[abs(C5) ≠ 1, abs(C5) + "z", "z"])
H3 = If(B3 ≟ 0, " ", If[B3 > 0, " + ", " - "])
H4 = If(B4 ≟ 0, " ", If[B4 > 0, " + ", " - "])
H5 = If(B5 ≟ 0, " ", If[B5 > 0, " + ", " - "])
F3 = If(A3  <  0, "- ", " ")
F4 = If(A4  <  0, "- ", " ")
F5 = If(A5  <  0, "- ", " ")
J3 = If(C3 ≟ 0, " ", If[C3 > 0, " + ", " - "])
J4 = If(C4 ≟ 0, " ", If[C4 > 0, " + ", " - "])
J5 = If(C5 ≟ 0, " ", If[C5 > 0, " + ", " - "])
N3: F3 + G3 + H3 + I3 + J3 + K3 + L3 + D3
N4: F4 + G4 + H4 + I4 + J4 + K4 + L4 + D4
N5: F5 + G5 + H5 + I5 + J5 + K5 + L5 + D5
text6: "SCD = \left\{\begin{array}{l}" + (LaTeX[N3]) + "\\" + (LaTeX[N4]) + "\\" + (LaTeX[N5]) + "\right."
text7: "solució:  \left\{\begin{array}{l}" + (LaTeX[$7]) + "\\" + (LaTeX[$8]) + "\\" + (LaTeX[$9]) + "\right."
G8 = If(B8 ≟ 0, " ", If[abs(B8) ≠ 1, abs(B8) + "x", "x"])
I8 = If(C8 ≟ 0, " ", If[abs(C8) ≠ 1, abs(C8) + "y", "y"])
K8 = If(D8 ≟ 0, " ", If[abs(D8) ≠ 1, abs(D8) + "z", "z"])
H8 = If(C8 ≟ 0, " ", If[C8 > 0, " + ", " - "])
J8 = If(D8 ≟ 0, " ", If[D8 > 0, " + ", " - "])
F8 = If(B8  <  0, "- ", " ")
N8: F8 + G8 + H8 + I8 + J8 + K8 + L8 + E8
G9 = If(B9 ≟ 0, " ", If[abs(B9) ≠ 1, abs(B9) + "x", "x"])
I9 = If(C9 ≟ 0, " ", If[abs(C9) ≠ 1, abs(C9) + "y", "y"])
K9 = If(D9 ≟ 0, " ", If[abs(D9) ≠ 1, abs(D9) + "z", "z"])
H9 = If(C9 ≟ 0, " ", If[C9 > 0, " + ", " - "])
J9 = If(D9 ≟ 0, " ", If[D9 > 0, " + ", " - "])
F9 = If(B9  <  0, "- ", " ")
N9: F9 + G9 + H9 + I9 + J9 + K9 + L9 + E9
G10 = If(B10 ≟ 0, " ", If[abs(B10) ≠ 1, abs(B10) + "x", "x"])
I10 = If(C10 ≟ 0, " ", If[abs(C10) ≠ 1, abs(C10) + "y", "y"])
K10 = If(D10 ≟ 0, " ", If[abs(D10) ≠ 1, abs(D10) + "z", "z"])
H10 = If(C10 ≟ 0, " ", If[C10 > 0, " + ", " - "])
J10 = If(D10 ≟ 0, " ", If[D10 > 0, " + ", " - "])
F10 = If(B10  <  0, "- ", " ")
N10: F10 + G10 + H10 + I10 + J10 + K10 + L10 + E10
A11 = NaN
B11 = NaN
D11 = NaN
text5: "SCI = \left\{\begin{array}{l} " + (LaTeX[N8]) + "\\ " + (LaTeX[N9]) + "\\ " + (LaTeX[N10]) + "\right."
text8: "solució:  \left\{\begin{array}{l} " + (LaTeX[$16]) + "\\" + (LaTeX[$17]) + " \\ " + (LaTeX[$18]) + "\right."
G13 = If(B13 ≟ 0, " ", If[abs(B13) ≠ 1, abs(B13) + "x", "x"])
I13 = If(C13 ≟ 0, " ", If[abs(C13) ≠ 1, abs(C13) + "y", "y"])
K13 = If(D13 ≟ 0, " ", If[abs(D13) ≠ 1, abs(D13) + "z", "z"])
H13 = If(C13 ≟ 0, " ", If[C13 > 0, " + ", " - "])
J13 = If(D13 ≟ 0, " ", If[D13 > 0, " + ", " - "])
F13 = If(B13  <  0, "- ", " ")
N13: F13 + G13 + H13 + I13 + J13 + K13 + L13 + E13
G14 = If(B14 ≟ 0, " ", If[abs(B14) ≠ 1, abs(B14) + "x", "x"])
I14 = If(C14 ≟ 0, " ", If[abs(C14) ≠ 1, abs(C14) + "y", "y"])
K14 = If(D14 ≟ 0, " ", If[abs(D14) ≠ 1, abs(D14) + "z", "z"])
H14 = If(C14 ≟ 0, " ", If[C14 > 0, " + ", " - "])
J14 = If(D14 ≟ 0, " ", If[D14 > 0, " + ", " - "])
F14 = If(B14  <  0, "- ", " ")
N14: F14 + G14 + H14 + I14 + J14 + K14 + L14 + E14
G15 = If(B15 ≟ 0, " ", If[abs(B15) ≠ 1, abs(B15) + "x", "x"])
I15 = If(C15 ≟ 0, " ", If[abs(C15) ≠ 1, abs(C15) + "y", "y"])
K15 = If(D15 ≟ 0, " ", If[abs(D15) ≠ 1, abs(D15) + "z", "z"])
H15 = If(C15 ≟ 0, " ", If[C15 > 0, " + ", " - "])
J15 = If(D15 ≟ 0, " ", If[D15 > 0, " + ", " - "])
F15 = If(B15  <  0, "- ", " ")
N15: F15 + G15 + H15 + I15 + J15 + K15 + L15 + E15
text9: "SI = \left\{\begin{array}{l}  " + (LaTeX[N13]) + "\\ " + (LaTeX[N14]) + " \\  " + (LaTeX[N15]) + "\right."
M: {{A3, B3, C3}, {A4, B4, C4}, {A5, B5, C5}}
text1: "\left| M \right| =" + (LaTeX[Determinant[M]]) + ""
P3: D3
P4: D4
P5: D5
Q3: B3
R3: C3
Q4: B4
R4: C4
Q5: B5
R5: C5
Cramer_x: {{P3, Q3, R3}, {P4, Q4, R4}, {P5, Q5, R5}}
metode: {"Cramer", "Gauss"}
U3: D3
U4: D4
U5: D5
T3: A3
T4: A4
T5: A5
V3: C3
V4: C4
V5: C5
Cramer_y: {{T3, U3, V3}, {T4, U4, V4}, {T5, U5, V5}}
X3: A3
X4: A4
X5: A5
Y3: B3
Y4: B4
Y5: B5
Z3: D3
Z4: D4
Z5: D5
Cramer_z: {{X3, Y3, Z3}, {X4, Y4, Z4}, {X5, Y5, Z5}}
text3: "x=\frac{\left| " + (LaTeX[Cramer_x]) + " \right| }{\left| " + (LaTeX[M]) + " \right| }=\frac{" + (LaTeX[Determinant[Cramer_x]]) + "}{" + (LaTeX[Determinant[M]]) + "}=" + (LaTeX[Determinant[Cramer_x] / Determinant[M]]) + " \space  \space ; \space  \space 
y=\frac{\left| " + (LaTeX[Cramer_y]) + " \right| }{\left| " + (LaTeX[M]) + " \right| }=\frac{" + (LaTeX[Determinant[Cramer_y]]) + " }{ " + (LaTeX[Determinant[M]]) + "}=" + (LaTeX[Determinant[Cramer_y] / Determinant[M]]) + " \space  \space ; \space  \space 
z=\frac{\left|" + (LaTeX[Cramer_z]) + "  \right| }{\left| " + (LaTeX[M]) + "  \right| }=\frac{" + (LaTeX[Determinant[Cramer_z]]) + "}{" + (LaTeX[Determinant[M]]) + " }= " + (LaTeX[Determinant[Cramer_z] / Determinant[M]]) + ""