Answer:
First, we write the augmented matrix.
⎡
⎢
⎣
1
−
1
1
2
3
−
1
3
−
2
−
9
|
8
−
2
9
⎤
⎥
⎦
Next, we perform row operations to obtain row-echelon form.
−
2
R
1
+
R
2
=
R
2
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
3
−
2
−
9
|
8
−
18
9
⎤
⎥
⎦
−
3
R
1
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
0
1
−
12
|
8
−
18
−
15
⎤
⎥
⎦
The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R
2
and \displaystyle {R}_{3}R
3
.
Interchange
R
2
and
R
3
→
⎡
⎢
⎣
1
−
1
1
8
0
1
−
12
−
15
0
5
−
3
−
18
⎤
⎥
⎦
Then
−
5
R
2
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
57
|
8
−
15
57
⎤
⎥
⎦
−
1
57
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
1
|
8
−
15
1
⎤
⎥
⎦
The last matrix represents the equivalent system.
x
−
y
+
z
=
8
y
−
12
z
=
−
15
z
=
1
Using back-substitution, we obtain the solution as \displaystyle \left(4,-3,1\right)(4,−3,1).First, we write the augmented matrix.
⎡
⎢
⎣
1
−
1
1
2
3
−
1
3
−
2
−
9
|
8
−
2
9
⎤
⎥
⎦
Next, we perform row operations to obtain row-echelon form.
−
2
R
1
+
R
2
=
R
2
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
3
−
2
−
9
|
8
−
18
9
⎤
⎥
⎦
−
3
R
1
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
0
1
−
12
|
8
−
18
−
15
⎤
⎥
⎦
The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R
2
and \displaystyle {R}_{3}R
3
.
Interchange
R
2
and
R
3
→
⎡
⎢
⎣
1
−
1
1
8
0
1
−
12
−
15
0
5
−
3
−
18
⎤
⎥
⎦
Then
−
5
R
2
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
57
|
8
−
15
57
⎤
⎥
⎦
−
1
57
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
1
|
8
−
15
1
⎤
⎥
⎦
The last matrix represents the equivalent system.
x
−
y
+
z
=
8
y
−
12
z
=
−
15
z=1
Using back-substitution, we obtain the solution as \displaystyle \left(4,-3,1\right)(4,−3,1).
Answer:
1 A
2 A
Step-by-step explanation:
1. steps can be positive whole numbers only
2. there is 15 steps
90 degrees
Hope this helps
Answer:
x=0.996
Step-by-step explanation:
To take natural log ln , we need to get e^2x alone
Subtract 5 on both sides
Now we divide both sides by 3
Now we take 'ln' on both sides
As per log property we can move exponent 2x before ln
The value of ln(e) = 1
Divide both sides by 2
x= 0.996215082
Round to nearest thousandth
x=0.996
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.<span><span>(<span><span>−∞</span>,∞</span>)</span><span><span>-∞</span>,∞</span></span><span><span>{<span>x|x∈R</span>}</span><span>x|x∈ℝ</span></span>Find the magnitude of the trig term <span><span>sin<span>(x)</span></span><span>sinx</span></span> by taking the absolute value of the coefficient.<span>11</span>The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.<span><span>y=<span>−1</span></span><span>y=<span>-1</span></span></span>The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.<span><span>y=1</span><span>y=1</span></span>The range is <span><span><span>−1</span>≤y≤1</span><span><span>-1</span>≤y≤1</span></span>.<span><span>[<span><span>−1</span>,1</span>]</span><span><span>-1</span>,1</span></span><span><span>{<span>y|<span>−1</span>≤y≤1</span>}</span><span>y|<span>-1</span>≤y≤1</span></span>Determine the domain and range.Domain: <span><span><span>(<span><span>−∞</span>,∞</span>)</span>,<span>{<span>x|x∈R</span>}</span></span><span><span><span>-∞</span>,∞</span>,<span>x|x∈ℝ</span></span></span>Range: <span><span>[<span><span>−1</span>,1</span>]</span>,<span>{<span>y|<span>−1</span>≤y≤1</span><span>}
</span></span></span>
