Answer: The required characteristic polynomial of the given matrix A is
Step-by-step explanation: We are given to find the characteristic polynomial of the following 3 × 3 matrix A with unknown variable x :
We know that
for any square matrix M, the characteristic polynomial is given by
where I is an identity matrix of same order as M.
Therefore, the characteristic polynomial of matrix A is
Thus, the required characteristic polynomial of the given matrix A is
Answer: The equation is y = 4x+3
Slope = 4
y intercept = 3
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Explanation:
Let's start off by finding the slope.
The slope is 4.
The y intercept is 3 because of the point (0,3)
We go from y = mx+b to y = 4x+3
m = slope
b = y intercept
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Check:
Plug in x = 0 and we should get to y = 3
y = 4x+3
y = 4(0)+3
y = 0+3
y = 3
That works out. Now try x = 4. It should lead to y = 19
y = 4x+3
y = 4(4)+3
y = 16+3
y = 19
The answer is confirmed.
John's method to determine the width of the stream uses the knowledge
that the tangent of 60° is approximately 1.7.
The proper sequence John would use to find the width of the stream are;
Reasons:
The steps that can be used to measure the width of the stream are;
Step 1: Drive a stake opposite the tree on the other side of the stream.
Step 2: With the aid of a compass, walk at right angles to the line formed by the stake and the tree.
Step 3; Keep walking along the previous path till a point is reached where the angle formed between the line of site to the tree and the walk path is 60°.
Step 4; At the point where the line of sight to the tree is 60°, a second stake is driven in the ground.
Step 5; Measure the distance between the stakes that are placed in the ground.
Step 6; Given that by trigonometry, the ratio of the width of the stream to the distance between the two stakes is tan(60°) ≈ 1.7, multiply the distance between the two stakes by 1.7 to find the width of the stream.
<em>The possible question options are;</em>
<em>John measures the the distance between the two stakes</em>
<em>John uses a compass to walk away from the stakes at a right angle</em>
<em>John multiplies the distance between the two stakes by 1.7 to find the distance</em>
<em>John drives a second stake in the ground</em>
<em>On the path John walks until he finds a line of sight to the tree that equals 60 degrees </em>
<em>John drives a stake opposite the tree to establish a line between two points.</em>
Learn more about trigonometric ratios here:
