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Why do square matrices only have multiplicative inverses?
there are pseudo inverses for non-square matrices a square matrix has an inverse only if the original matrix has full rank which implies that no vector is annihilated by the matrix as a multiplicative operator
When the dimensions of a triangle are tripled is the area of the new triangle 6 times greater than the original triangle?
No. It's 9 times greater. The area changes according to the square ofthe number that you use to multiply all the linear dimensions."3 squared" = 32 = 3 x 3 = 9If you made the dimensions of the triangle 10 times bigger, the areawould become 102 = 100 times greater.
A triangle is dilated with a scale factor of 2 If the area of the original triangle is 9 square inches what is the area of the image in square inches?
Area is proportional to the square of the linear dimensions. If the linear dimensions are doubled, the area is increased by a factor of 22 = 4. The new area is 9 x 4 = 36 square inches.
When each side of a given square is increased by 4 feets the area is increased by 64 feet determine the dimensions of original square?
Suppose the length of a side in the original square was S feet, so that the original area was S2 square feet. The incresed side is (S+4) feet [not feets!] giving a new area of (s+4)2 sq feet. So (S+4)2 = S2 + 64 S2 + 8x + 16 = S2 + 64 8S = 48 and so S = 6 ft
How do you solve simultaneous equations using matrices?
There are many ways of doing this. For example Gaussian elimination, diagonalising, but the simplest to explain is matrix inversion (I'm assuming some knowledge of matrices here, and unfortunately some of the matrix formatting is a little off due to limitations in the editor): Any system of simultaneous equations can be rewritten as the matrix equation A.v = u The coefficients of the variables become the entries in the square matrix, A. To solve the matrix equation we need to invert A, and then multiply by the inverse, giving us I.v = A-1.u where I is the identity matrix. As an example take the following system of equations: 2x - 3y = 1 4x - 5y = 5 The matrix version of this equation is { 2 -3 } { x } = { 1 } { 4 -5 } { y } { 5 } A v u It's clear that if you multiply out the matrix row by row, you get the original set of equations. In our case I = { 1 0 } { 0 1 } A-1 = { -2.5 1.5 } { -2 1 } (Finding the inverse of a matrix is a whole other question) so A-1.u = { 5 } { 3 } Therefore we have x = 5, and y = 3. Inversion of A is the most difficult step, though this can easily be done with a computer.
What is the proof of the anticommutator relationship for gamma matrices?
The proof of the anticommutator relationship for gamma matrices shows that when you multiply two gamma matrices and switch their order, the result is the negative of the original product. This relationship is important in quantum field theory and helps describe the behavior of particles.
Why do square matrices only have multiplicative inverses?
there are pseudo inverses for non-square matrices a square matrix has an inverse only if the original matrix has full rank which implies that no vector is annihilated by the matrix as a multiplicative operator
What sequence is formed by subtracting each term of a sequence from the next term?
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
How you could use the dimensions of a reduced rectangle and one given measurement of an original rectangle to find a missing measure?
To find a missing measure of the original rectangle, you can use the dimensions of the reduced rectangle, which are scaled down versions of the original's dimensions. If you know one measurement of the original rectangle (either length or width), you can set up a proportion using the corresponding dimensions of the reduced rectangle. By solving for the missing measurement, you can determine the original rectangle's dimensions. This method relies on the fact that the ratio of the sides of the reduced rectangle remains constant with respect to those of the original rectangle.
How were the dimensions of the original Globe agreed upon by historians?
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What are the key differences between DS1 clones and their original counterparts?
The key differences between DS1 clones and their original counterparts are that clones are genetically identical copies of the original organism, while the original counterparts are the organisms from which the clones were derived. Clones have the same DNA as the original, but may exhibit differences in traits due to environmental factors or genetic mutations.
When a vector is multiplied by a scalar physical quantitythen what will be dimensions of resulting vector?
The same as the original vector. The scalar will change the numbers, but not the dimensions.
What is the reverse of add 310?
The reverse of adding 310 is subtracting 310. If you start with a number and add 310, you can return to the original number by subtracting 310 from the result. This operation effectively undoes the initial addition.
What is the raven standard progressive matrices?
Raven Standard Progressive Matrices: These were the original form of the matrices, first published in 1938. The booklet comprises five sets (A to E) of 12 items each (e.g., A1 through A12), with items within a set becoming increasingly difficult, requiring ever greater cognitive capacity to encode and analyze information. All items are presented in black ink on a white background
How is porcelain now different from original porcelain?
There are no differences
What is the principal reduction formula used to calculate the decrease in the original loan amount?
The principal reduction formula calculates the decrease in the original loan amount by subtracting the payment made towards the principal from the original loan balance.
What would be the dimensions of a new right rectangular prism that has Y fewer unit cubes than the original prism?
To find the dimensions of the new right rectangular prism with Y fewer unit cubes than the original prism, first determine the volume of the original prism, which is the product of its length, width, and height (V = l × w × h). Subtract Y from this volume to get the new volume (V' = V - Y). The new prism can have various dimensions that multiply to this new volume, depending on how you choose to adjust the length, width, or height while maintaining the rectangular shape. Specific dimensions will depend on the original dimensions and the value of Y.
