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yKpoI14uk [10]
3 years ago
8

Fill in the blanks using place value: 43 ones x 3 tens =_______tens

Mathematics
1 answer:
KonstantinChe [14]3 years ago
7 0
129







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10. (a) Consider the following matrices: A = ( 2 ) B = (3) and C = (-3) w = Find the det(A). [1] (ii) Is the matrix A singular?
Viefleur [7K]

i) We have to find the determinant of A.

We can do this as:

\det(A)=|\begin{bmatrix}{3} & {6} \\ {1} & {-2}\end{bmatrix}|=3*(-2)-6*1=-6-6=-12

ii) We have to find if the matrix A is singular.

Singular matrix have determinant equal to 0.

This is not the case for A, as its determinant is -12. Then, A is not a singular matrix.

iii) We have to find the values of x and y so that AB = C.

We have to write the matrix multiplication and we will obtain a system of linear equations:

We can now solve the system of equations by adding 3 times the second equation to the first equation:

\begin{gathered} 3(x-2y)+(3x+6y)=3(-3)+(-3) \\ 3x-6y+3x+6y=-9-3 \\ 6x+0y=-12 \\ x=\frac{-12}{6} \\ x=-2 \end{gathered}

We can now use the second equation to find the value of y:

\begin{gathered} x-2y=-3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ y=\frac{-2+3}{2} \\ y=\frac{1}{2} \end{gathered}

The values are x = -2 and y = 1/2.

iv) When we want to multiply two matrices, the required condition is that the number of columns of the matrix on the left is equal the number of rows of the matrix on the right.

In the case of A(2x2) and B(2x1), when we do A*B this condition is satisfied.

But when we try to multiply BA, the number of columns of B is not equal to the number of rows of A, so the matrix mulitplication is not possible.

Answer:

i) det(A) = -12

ii) A is not singular because singular matrices have determinant equal to zero.

iii) x = -2 and y = 1/2.

iv) Is not possible because the number of columns of the first matrix has to be equal to the number of rows of the second matrix.

6 0
1 year ago
4 Jarome needs to have at least $150 to open his own checking account. He has already saved $30 and plans to earn more money by
anastassius [24]

Answer:

how much does he get from each house

Step-by-step explanation:

7 0
3 years ago
Subtract.
Rom4ik [11]
(2x + 2) - (3x + 11)
Remove the parentheses
2x + 2 - 3x + 11
And then combine like terms
So the answer is:
-x - 9
7 0
3 years ago
Please help! 30 points!
Rashid [163]

Answer: 64.2^{\circ}

Step-by-step explanation:

According to the cosine rule

\cos C=\dfrac{a^2+b^2-c^2}{2ab}

Here, a=83, b=111, c=165,\ C=180^{\circ}-\theta

Putting values

\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}

So, the ship turns by 64.2^{\circ} north of west

8 0
3 years ago
What is the slope of the line on the graph below?
Elena L [17]

Answer: The answer is 1/3

5 0
2 years ago
Read 2 more answers
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