Vector Algebra Class 12 Important Questions Pdf Download

CBSE Class 12 Mathematics Vector Algebra Extra Questions. myCBSEguide has just released Chapter Wise Question Answers for class 12 Maths. There chapter wise Practice Questions with complete solutions are available for download in myCBSEguide website and mobile app. These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. There are around 4-5 set of solved Chapter 10 Vector Algebra Mathematics Extra Questions from each and every chapter. The students will not miss any concept in these Chapter wise question that are specially designed to tackle Board Exam. We have taken care of every single concept given in CBSE Class 12 Mathematics syllabus and questions are framed as per the latest marking scheme and blue print issued by CBSE for class 12.

The below mentioned pdf consist of Important questions of class 12 maths for chapter-10 as per NCERT with detail solutions and added MCQ based questions. Check out other chapters of Important questions for CBSE class 12 Maths prepared by Physics Wallah. Solve NCERT Textbook exercise with the help of NCERT Solutions for class 12 Maths Prepared by Experts of Physics Wallah.

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Data from thousands of transcription-profiling experiments in organisms ranging from yeast to humans are now publicly available. How best to analyze these data remains an important challenge. A variety of tools have been used for this purpose, including hierarchical clustering, self-organizing maps and principal components analysis. In particular, concepts from vector algebra have proven useful in the study of genome-wide expression data.

Here we present a framework based on vector algebra for the analysis of transcription profiles that is geometrically intuitive and computationally efficient. Concepts in vector algebra such as angles, magnitudes, subspaces, singular value decomposition, bases and projections have natural and powerful interpretations in the analysis of microarray data. Angles in particular offer a rigorous method of defining 'similarity' and are useful in evaluating the claims of a microarray-based study. We present a sample analysis of cells treated with rapamycin, an immunosuppressant whose effects have been extensively studied with microarrays. In addition, the algebraic concept of a basis for a space affords the opportunity to simplify data analysis and uncover a limited number of expression vectors to span the transcriptional range of cell behavior.

A related need that has been less addressed is the systematization of expression data analysis. This requirement extends not only to analysis but also to pedagogy and to practical aspects of algorithm implementation. Various studies in the literature have successfully implemented tools from vector algebra in analyzing genome-wide expression data [11,15,16]. However, a framework for the analysis of transcription profiles using vector algebra has not yet been codified. Here we present such a framework. Common statistical measures have natural counterparts in vector algebra that have visual interpretations and are easily implemented on a computer. Within this framework, the analysis of genome-wide expression data is converted to the study of high-dimensional vector spaces. The many powerful theorems that have been developed in vector algebra can be applied to these spaces, and these theorems offer biologically relevant insights. Elements of the vector space can also be analyzed statistically. This construction has analytic and pedagogic appeal.

There is another, complementary, way of thinking about expression profiles, or more generally, about multivariate statistical data [17]. Although analysis of gene vectors is a powerful tool, it is less efficient at demonstrating relationships between profiles. This is because overlaying clouds of thousands of gene vectors may not offer an insightful picture because of the many data points in view. In the alternative method of analysis, an expression profile is regarded as just one point in a high-dimensional space. Because this point captures the same information contained in the scatterplot of gene vectors, the point must reside in a much higher-dimensional space. In this space, the relationships between profiles become more apparent. Instead of plotting genes, one now plots experiments (Figure 1c). As new profiles are added to the data matrix, the dimension of the space remains fixed but the number of points increases, the reverse case of gene vectors. Although the high-dimensional space of experiment vectors cannot be visualized, the relationships of vectors in the space can often be understood using intuition from the two- or three-dimensional case. The power of vector algebra comes from its ability to scale - the concepts, equations and theorems move seamlessly (usually identically) to higher dimensions.

The vector algebra approach is illustrated using a publicly available data set. The small molecule rapamycin has been transcriptionally profiled by three research groups in four separate studies [4,11,21,22]. It has a very dramatic expression profile in which hundreds of genes are rapidly (within minutes) up- or down-regulated. The protein targets of rapamycin (the Tor proteins) are known to sense nutrients. When treated as an experiment vector, other experiment vectors were searched for that had a low angle with the rapamycin vector. Against the same set of 300 diverse expression profiles described earlier [19], not a single vector could be found that had an angle less than 60 with the rapamycin experiment vector (data not shown). However another study identified two vectors with smaller angles to the rapamycin expression vector (angles of 44 and 47) [11]. These similar vectors were those corresponding to the removal of high-quality carbon or nitrogen from the media. Thus, it can be inferred that the Tor proteins regulate the responses to carbon- and nitrogen-quality of the medium. This is an example of using angles to identify the functions of uncharacterized proteins.

An advantage of vector algebra is the extension from angles into ratios of magnitudes for which other formulations have awkward or no counterparts. The two four-dimensional vectors x = [1 0 2 -1]T and y = [2 0 4 -2]T have = 0 (implying r = 1). However, there is an important difference between the vectors not identified by these measures, as we can observe that y = 2x. This information is captured by computing the ratio of vector magnitudes.

Another advantage to treating expression data as vectors in a space rather than as n-tuples is the associated notion of subspaces. With experiment vectors, this concept is particularly valuable. Experiment vector space can be divided into subspaces, most naturally where the subspaces correspond to co-regulated or functionally related genes. This can most easily be done using annotated lists where genes are classified by function. The Munich Information Center for Protein Sequences (MIPS) provides a commonly used functional grouping for genes [23].

One of the most powerful ideas in linear algebra is the notion of basis vectors. Besides constructing the space, basis vectors can be chosen to highlight important features of the data or simply to store the data efficiently. For example, the function sin x can be expressed either in a polynomial or exponential basis,

The first basis is clearly awkward - it is infinite-dimensional and offers little insight. However, the second basis captures the sine wave more compactly and provides more insight. Many of the successes of vector algebra in image compression, smoothing and signal detection come from the identification of appropriate basis functions.

We have described various techniques motivated by vector algebra for analyzing genome-wide expression data. Some of these techniques have been used previously, but we find that by regarding expression profiles as vectors, either in the sense of genes or experiments, we gain a richer understanding of the existing techniques and can take these insights into new directions.

Vectors algebra is the branch of algebra that involves operations on vectors. Vectors are quantities that have both magnitude and direction so normal operations are not performed on the vectors. We can add, subtract, and multiply vector quantities using special vector algebra rules. Vectors can be easily represented in 2-D or 3-D spaces. Vector algebra has various applications it is used in solving various problems in mathematics and physics, engineering, and various other fields.

Vector algebra is the type of Algebra that is used to perform various algebraic operations on vectors. As we know vectors are quantities that have both magnitude and direction whereas scalar quantities only have magnitude and no direction. The difference between vector quantities and scaler quantities can be understood with the help of the example discussed below.

Such quantities in which direction are present are called Vector quantities. Examples of vector quantities are Displacement, Velocity, Force, etc. As these quantities have directions operations on these quantities are not easily applied and the concept of vector algebra is used to perform operations on these quantities.

We use various formulas in Vector Algebra to solve various types of complex problems. These formulas are very helpful in understanding and solving vector algebra problems. The important vector algebra formulas are,

Vector algebra is widely used in various fields such as Mathematics, Engineering, Physics, and others. Various physical quantities encountered by us in real life such as force, acceleration, velocity, and others are vector quantities and we use vector algebra to define and operate on those quantities. Some of the important applications of vector algebra are

As we know that vectors are quantities that have both magnitude and direction. So it is not easy to directly apply mathematical operations to them, the algebra which deals with the vector is called vector algebra. ff782bc1db