We eliminate one variable using row operations and solve for the other. Say that we wish to solve for
If equation (2) is multiplied by the opposite of the coefficient of
in equation (1), equation (1) is multiplied by the coefficient of
in equation (2), and we add the two equations, the variable
will be eliminated.
Now, solve for
Similarly, to solve for
we will eliminate
Solving for
gives
Notice that the denominator for both
and
is the determinant of the coefficient matrix.
We can use these formulas to solve for
and
but Cramer’s Rule also introduces new notation:
determinant of the coefficient matrix
determinant of the numerator in the solution of
determinant of the numerator in the solution of
The key to Cramer’s Rule is replacing the variable column of interest with the constant column and calculating the determinants. We can then express
and
as a quotient of two determinants.
Cramer’s rule for 2×2 systems
Cramer’s Rule is a method that uses determinants to solve systems of equations that have the same number of equations as variables.
Consider a system of two linear equations in two variables.
The solution using Cramer’s Rule is given as
If we are solving for
the
column is replaced with the constant column. If we are solving for
the
column is replaced with the constant column.
Finding the determinant of a 2×2 matrix is straightforward, but finding the determinant of a 3×3 matrix is more complicated. One method is to augment the 3×3 matrix with a repetition of the first two columns, giving a 3×5 matrix. Then we calculate the sum of the products of entries
down each of the three diagonals (upper left to lower right), and subtract the products of entries
up each of the three diagonals (lower left to upper right). This is more easily understood with a visual and an example.
Find the
determinant of the 3×3 matrix.
Augment
with the first two columns.
From upper left to lower right: Multiply the entries down the first diagonal. Add the result to the product of entries down the second diagonal. Add this result to the product of the entries down the third diagonal.
From lower left to upper right: Subtract the product of entries up the first diagonal. From this result subtract the product of entries up the second diagonal. From this result, subtract the product of entries up the third diagonal.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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