Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
![\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%260%260%5C%5C0%261%260%260%5C%5C0%260%261%260%5C%5C0%260%260%261%5Cend%7Barray%7D%5Cright%5D)
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
![\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%260%260%26a%5C%5C0%261%260%260%26b%5C%5C0%260%261%260%26c%5C%5C0%260%260%261%26d%5Cend%7Barray%7D%5Cright%5D)
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).
Answer: A) -4
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Explanation:
The 3^0 in the denominator is equal to 1. Any nonzero number raised to an exponent of 0 is always 1. So this equation x^0 = 1 is true when x is nonzero.
This allows us to simplify to the equation 3^x = 1/81
Note how 81 = 3^4. Taking the reciprocal of 81 means the exponent goes from positive to negative. So 3^(-4) = 1/81. The rule is x^(-k) = 1/( x^k ). We could use logarithms to solve 3^x = 1/81.
Answer:
Step-by-step explanation:
12.
Statements:
1. RS bistecs PQ at T; PQ bisects RS at T.
2. RT is congruent to ST; PT is congruent to QT.
3. Angle T is congruent to angle T.
4. Triangle PTS is congruent to triangle QTR.
Reasons:
1. Given.
2. Definition of a bisector of a line segment.
3. Reflexive Property.
4. SAS Postulate
13.
Statements:
1. AB is congruent to AD; AC bisects angle BAD.
2. Angle BAC is congruent to angle DAC.
3. AC is congruent to AC.
4. Triangle ABC is congruent to triangle ADC.
Reasons:
1. Given.
2. Definition of a bisector of an angle.
3. Reflexive Property.
4. SAS Postulate.
Answer:
4³
Step-by-step explanation:
{(2)²}⁷/{(2)²}¹⁰
2¹⁴/ 2²⁰
Using property...
2¹⁴-²⁰= 2-⁶
Hence....
(-2)×(-2)×(-2)×(-2)×(-2)×(-2)= 64
So...
64=4³
hope it helps
Answer:
Step-by-step explanation:
take 51 degree as reference angle
using sin rule
sin 51=opposite/hypotenuse
0.77=YZ/9
9*0.77=YZ
6.93=YZ
6.9=YZ